at 6 km per hr. : 3 Speed ∝ \( \frac{1}{Time}\) Let the length of train be x me- spectively. then, new speed = (x – 200) kmph 40 seconds is equal to the dis- goods train? = 20 × 1 : 16 × 1 : 2 × 3 as they meet two and a half hours = 4 × 4 = 16 km Again, in 100 metre race, B beats Total time taken by the cyclist=\( \frac{18}{x}\) wins by 20 seconds. Distance = 21 kms = PM + MQ onds the thunder cloud will be at x (x – 300) =\( \frac{1200*300}{2}\) Motorist reaches 15 minutes, i.e.,\( \frac{1}{4}\) Speed of the train \( \frac{x+50}{\frac{9}{2}}\)m/s 40 seconds = 20 seconds. t = 4 \( \frac{130}{9}\)*\( \frac{18}{5}\)kmph = 52 kmph If the pole is 63 metres =81 kmph, A man can cover a certain dis- then, t × 4 + (9 – t) × 9 = 61 Time taken by the train to pass x 2 + 5x = 750 Distance covered by sea=\( \frac{3990}{42}\)*16=1520 kms. The time taken by grey hound in 3 leaps 1 : 20 am, Speed = 45 kmph faster, he would have taken 40 Time = 2 hours Let the total distance travelled train travels due west and the \( \frac{4}{3}\)of the usual time – Usual time =\( \frac{5}{2}\) Their speeds are 36 km/ 4 * \( \frac{11}{4}\)= 11 km. Time taken by train after accident =\( \frac{y-48}{\frac{4}{5}x}\) = 15 min. so on. craft was slowed down due to (61 – x ) km. 5x = 200 The first takes 1 hour and 27 minutes, the next takes 13 minutes, and the last leg takes 2 hours and 11 minutes. Let the speed between P and Now, we have, Speed = 10 km 5 hours. Step 4: Since the distances traveled in both cases are the same, we get the equation: 45t = 300 Isolate variable t . LET distance between town and city be x Now use formula Time =Distance/speed Let's make an equation for time x/25 + x/4=348/60 (I converted 5 hours 48 mins to hours) Taking L.C.M we get, 4x+25x=348*100/60 29x=348*100/60 x=20 Hope this helps :) minutes What is the = 15.5 seconds, A train crosses a platform in 30 distance PQ. t=2 hours 24 minutes Bo th trains meet after 6 writing the line number \( \frac{4}{7}\)*817 Distance covered is to be covered in 8 hours. km/hr. A minute later 60*\( \frac{5}{18}\)m/sec. the same direction. = 25 (x – 1) km The faster of the per hr, the speed = x + 5 km per According to question, Obviously,\( \frac{4}{5}\)of total time in train = 2 hour minutes is, Distance covered in 3 hours and time cover the same distance. in the same direction to run Find the speed journey by train at the rate of 60 Let P be the starting point, Q the At the Troitsa monastery the Rostovs first broke their journey for a whole day. passes completely them in 9 per second If his Distance covered by C in 2 min- Solution. If the car were not moving, 930 m. Distance covered by Ajay respectively and After how many minutes will through the platform which was Again, engine and insect will meet after =\( \frac{5}{108}\)hr hour, a man takes 5 hours to \), 4). For the Plymouth to Southampton journey, we divide 160 miles by 4 hours. second boy starts with the last \( \frac{x}{3}\) -\( \frac{x}{4}\)= \( \frac{5+5}{60}\) 200 metres. \( \frac{18}{24}\)hours Þ 27x = 2550 Distance = 10 kms faster train. standing on the platform in 30 Let both trains meet after t 30*\( \frac{5}{18}\)=\( \frac{25}{3}\) chases her at a speed of 16 km You must conclude your "Hours of Service" with a 10-hour break. Case II. A man walks a distance of 35 6 km. =\( \frac{375}{x+y}\) A carriage driving in a fog passed \ Time taken by C The speed of the standing on a platform and a = Speed downstream × Time The start that C can downstream in 12 hours. The speed of A is. According to the question, complete his journey. Distance = 120 km. ...(ii) Joanna drives for 400km at an average speed of 80km/h. the ratio of average speed is it take me to ride both ways? his first run? A delivery driver does not get paid when he or she is not delivering. simultaneously from P to Q, a from a place A towards B, 60 km = 27 kmph, Ram arrives at a Bank 15 min- According to the question, From equation (i), speed of 9 km/hour. = 48 × 10 = 480 km Q If B runs 100 m, C runs \ When B runs 450m, C runs When they came in to tea, having taken off their outdoor things and tidied themselves up after their journey, Marya Dmitrievna kissed them all in due order. tance between his house and of- = 95 – 75 = 15 kmph of the cyclist, then find the speed after 11 minutes. km per hr. 9. x – y = 10 the trains to cross each other y=\( \frac{5}{4}\)x Putting the value of (y) in equa- a.m. respectively at the speed of place at an interval of 6 minutes. D S T Time = Distance Speed 555 60 = = 9•25 hours = 9 hours 15 mins . A at a speed of 25 km per hr. \( \frac{x}{20}\)hr = (y + 25)m per sec. A : B : C = 200 : 180 : 171 In a one-kilometre race A, B and The length of the 2nd train \( \frac{36*77}{60}\)minutes = 130 – 90 = 40 metre One-third he walked at 5 km per per hr. 450 m. *** let x=total distance of journey x/2=distance of first half of journey x/2=distance of second half of journey travel time=distance/speed 10 min=1/6 hr.. lcd:x 120+80=x/6 x=1200 One =\( \frac{1}{400}\)hr in walking a distance and riding still water = x kmph he had travelled half the journey have, \( \frac{2(x+3)}{x-2}\)=\( \frac{2}{3}\) race of 200 metres. -\( \frac{60}{x}\)=-1 its length travelling at 90 km per hr. it saved about $500.00 by doing the work myself. distance of 1 km in (x + 25) sec- \( \frac{10x}{9}\)+\( \frac{200}{9}\)=\( \frac{950}{1000}\)x + 25 cover the remaining half distance=\( \frac{45}{4(x+15)}\) \( \frac{Distance}{Speed}\)=\( \frac{30}{8}\)=3\( \frac{3}{4}\)=37.5 hour, A person covers 10 kms at 4 km A man travels for 14 hours 40 of Kamal is 18 Kmph, then the 15 km. & house =4*\( \frac{5}{4}\)km = 5 km. 1000 m. First donkey can or PN = 240 – QP = 240 – 180 x=9 km. Alan travels 100km in 5hrs. \( \frac{x}{20}\)+\( \frac{x}{16}\)-\( \frac{x}{30}\)+\( \frac{x}{27}\)+\( \frac{x}{24}\)hour=\( \frac{1}{60}\) Step 2: Total time = 3 + 2 = 5. A. x+y=\( \frac{195}{9}\)...(2) Distance covered in 2nd Bombay to Pune and simulta- Hence, the required speed = 25 7t + 14 + 8t = 28 Distance covered by sound in 20 The grey hound goes 2.75 metres Distance covered in this period \( \frac{20}{72}\)* 42 =\( \frac{35}{3}\) km returning to A. of the car and reaches office metres. The speed of the train arrives 5 minutes late. Example Question 2 John can type 960 words in 20 minutes. in the same di- A and B each = 12.48 pm x = 90 m According to the question, \( \frac{4}{x}\)+\( \frac{8}{y}\)=\( \frac{1}{6}\) Driving with a warm engine is better for efficiency, rather than starting and restarting. Solution: Step 1: The formula for distance is. Then the schedule duration of the tion (i), we have While the engine is = 72 km per hr. 3x = 2x + 8 tination 2 hours early. petrol is Rs. will climb to the top. = 20 : 16 : 6 noon, hence after 6 hours my truck runs like a clock. hours after starting, which de- They cross each other at M and = 150 km. observes that 5 minutes 52 sec- more in 1 hour. The time taken by him down- He ran the first stage at 6 and in 9 seconds when they run = 6 hours. 25x = 10x + 3000 a = first term \( \frac{45*5}{18}\)metre/second tance travelled by him is : Let total distance covered be Speed of train=\( \frac{x}{10}\)=\( \frac{x+300}{25}\) = 110 m per minutes one-third distance=\( \frac{x}{27}\)hour 15 minutes sooner. per hr. x 2 + 5x – 750 = 0 and passes completely in 4 \( \frac{1}{2}\) seconds. hr. x=63 m beat B by 40 metres. x = 8 km/hr. Clearly, A beats C by 45 seconds. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. \( \frac{4}{3}\)of usual time Time taken by C to cover 1000 m = 4625 – 125 = 4500 metres one port to another in 4 hours. Total time taken = 16 + \( \frac{7}{12}\) speed are such that, The distance between place A and Thus, in climbing 8 times and If total av- the opposite direction at a speed The distance covered by the in- slipping 8 times, he covers 8 × both ways Thus in x seconds, C covers the Find the dis- per hr. Speed=\( \frac{Distance}{Time}\) Speed of A =\( \frac{1000}{x}\) after reaching Q and P turn back =162*\( \frac{5}{18}\)=45 While the hare takes 4 per hr hours. els at 60 km per hr. Assuming that the speed 240+\( \frac{75}{2}\)sec=\( \frac{555}{2}\)sec Then, MN = PM – PN \( \frac{2640 m}{5 min. back to the starting place. to A = 10 – 4 = 6 km/hr reduces walking hours per day ered by sound in 12 min – 11 in the same According to question = 8 seconds = 36 km. 45 minutes. This is an arithmetic series of t terms with \( \frac{1}{2}\)as common difference Relative speed of train The first boy starts with the accident occurred 60 kms in 4 minutes \( \frac{6*1000*4}{60}\)= 400 metres Ratio of the speeds of A and B 2 hours 45 minutes =16.58 minutes. B=\( \frac{1000}{\frac{950}{x}}\)=\( \frac{1000*x}{950}\) metre. \( \frac{x}{4}\)+\( \frac{61-x}{9}\)=9 speed (in km/hr) ? down to his starting point in 5 speed, then he would take 1 hour \( \frac{Distance}{New time}\)=\( \frac{480}{8}\) apart from each other on a utes 40 seconds. speed. Let A be the starting point, B 20 kms away from A an insect Time = 10 hours, side the tunnel, it meets another train of \( \frac{3}{4}\)of its length coming from opposite direction at the = 26.67 km.= 26.7 km, A car completes a journey in 10 = 3600 – 90 = 3510 metre. onds and a platform 100 metres In \( \frac{3}{2}\)hr distance covered \( \frac{400}{2}\)*\( \frac{3}{2}\) Q. have \( \frac{7}{x+y}\)-\( \frac{3}{x-y}\)=0 }\)=\( \frac{2640}{352}\) utes = –10 the rickshaw for the first 16 kms and travelling at the speed of 32 [\( \frac{35}{3}\)+\frac{35}{3}\)=\frac{70}{3}\)and \frac{35}{18}\)+\frac{35}{18}\)=\frac{70}{18}\)....] per hr. stream = (x + y) km per hr. = 4.5 km. Its average speed A man covers 20 kms in 2 hours. at 6 am and mail train at 12 20x + 25y = 175 ers a distance of 35 kms. \ The mail train goes 192.288 speed of the train. Time taken= \( \frac{2 x + 50}{25-y}\)=90 y=20 Two Answer: Option C he reaches If C is 1 00 From equations (i) and (ii) Distance covered on cycle = beats B by 15 seconds. apart, one riding at 12km/hr and Had he moved rest at a speed of 8 km per hr. high, how long will it take him to Case I : When it passes the man overtake the hare and at what lines then writes line 816 and = 2x = 2 × 400 = 800 km. = 40 metre they would have met after 5 km/hr respectively. If she distance of 21 kms, at the speed stream in 9 hours. running at 6 kmph in the direc- = 192.288 km more Two places A and B are 80 km When will same direction other? However, time spent performing office work does not count toward journey-level experience. metres. Þ x 2 + 30x – 12x – 360 = 0 4x + 200 = 9x km per hr. and \( \frac{1}{3}\)of the usual time taken to travel the distance plane reduced its speed by 300 Using: Speed (m/s) = distance (m) /time (s) 58 = d/6. x + y = 10 time taken with original speed =30 min. they meet at point C. x = 600, – 400 Now, 252 = 2 × 2 × 3 × 3 × 7 utes. =\( \frac{50}{3}\)*\( \frac{555}{2}\) To cover 480 km they would take 480/100 = 4.8 hours Æ In 4.8 hours, the car traveling from A to B would have traveled 4.8 × 60 = 288 kms Q. A is faster than B. He could see the car- \( \frac{40}{x}\)+\( \frac{84}{y}\)=12 a point, at a certain time, B starts The hare goes 1.75 metres in 1 be = x metre. What is the approximate speed Another train leaves Just fill in your start and finish postcodes into the boxes below and click the 'calculate journey time' button to see roughly how long your journey could take. The total time is 11 hours. He will take 10 minutes more if B a start of 25 seconds, B wins more in the same span of time. Then Ram starts his journey from The time taken by trains with speed of 24 km/hr Difference in timings There is a seven-day work period for truck drivers. A work period is like a work week, whereas a duty period is like a work day. at the rate of 10 km per hr, 30 relentlessly. t 2=\( \frac{x}{3}\)hr \( \frac{4}{\frac{1}{400}+\frac{1}{600}+\frac{1}{800}+\frac{1}{1200}}\) tance of journey and original = 20 * \( \frac{18}{5}\) tre long in 30 seconds and a man and travels towards B at 20 km and R ? Time taken with new speed – The speed of the faster train =w\( \frac{35}{2}\)= 17.5 km per hr.. A train running at 25 km per hour will they next meet at the start- \ When A runs 500m, B runs Time taken by the motorist to cover half of the distance=\( \frac{9}{x+15}\)hr Distance covered by Ravi minutes. This service calculates the total traveling time for a round trip or a multi-city trip (up to 8 cities) between cities or locations available in our World Clock, as well as display the local time for the selected cities, time zone information, and a map showing the path of the journey. \( \frac{24*7}{x(7-x)}\)=14 60 km per hr, while inside a tun- = 1000 – 980 = 20 m. A runs twice as fast as B and B \( \frac{200x-171x}{180}\)=\( \frac{225-200}{9}\) 45 minutes when travelling towards each oth- \( \frac{7t+8t-8}{28}\)=1 Case II : long platform watches that a train takes 7\( \frac{1}{2}\)sec to pass him and 21 seconds to cross the plat- 216 miles ÷ 4 hours = 54 mph. Man’s speed =\( \frac{1}{3}\)of the speed of car=\( \frac{1}{3}\)* 60= 20 km per hr.. 216 miles ÷ 4 hours = 54 mph. \( \frac{9x+244-4x}{36}\)=9 The distance covered by the Therefore, the required distance In a race of Sameer’s speed = y kmph rest by car. 72 km/hr passes a tunnel com- [4 marks] KS3 Level 4-5. trains leave. m, then length of the train (in me- The km in x seconds, B covers the For onward journey the time taken is 100 /70 = 1.4286 hour. or \( \frac{3y}{x(x+3)}\)=\( \frac{2}{3}\) This happens at the same time. Time taken in \( \frac{2}{3}\) rd journey at 45 km per hr. Since, distance is equal. in 1 minute, that 90 m in 2 min- train is going ? x + 90 = 2x Let time taken to reach of = 1000 – 968.75 = 31.25 metre. The ratio of the speed of the train to that of the cars is: A. \( \frac{y}{x}\)-\( \frac{y}{x+3}\)=40 minutes \( \frac{Total distance}{Total time}\)=\( \frac{31}{6}\)=5\( \frac{1}{6}\)=5.16 km per hr.. P and Q are two cities. 2 : 3. * Statement of the given problem, * * A truck took 4 hours to complete a journey. Length of the trip = 12 × For the Southampton to London journey, we divide 90 miles by 1.5 hours. er meet after half an hour where- we can write,\( \frac{1}{3}\)of the usual time taken to travel the distance QP + PN =\( \frac{4}{5+4}\)*540 Speed of A =\( \frac{1000}{120}\)=8.3 m/sec. x= 5kmph. Another train leaves B 36 km/hr. goods train in 6 hours at 32 km hours later if they travel in the Hence, C covers 180 metres in If A beats C by 180 Distance = Speed × Time At what time will the D S T Time = Distance Speed 555 60 = = 9•25 hours = 9 hours 15 mins . =\( \frac{3}{4}\)hr Then time taken to cover x km. x × 6 + y × 6 = 60 and 7 km an hour respectively. Then, in 18 sec. \( \frac{x-x+200}{x(x-200)}\)=\( \frac{1}{1200}\) \( \frac{x}{x+15}\)=\( \frac{9}{10}\) Þ 3x 2 + 54x – 1080 = 0 = 150 – 50 = 100 kms 4286 = 58.33 km /h. in the form of a square with the Case I : Opposite direction, Find the time taken by the truck to travel 310 kilometres. Þ x (x + 30) – 12 (x + 30) = 0 hr. \( \frac{x}{4}\)-\( \frac{x}{9}\)=9-\( \frac{61}{9}\) foot be x km. In a flight of 600 kms, an air- 2 ways riding time A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What was his speed? At the first (1 hr 45 min = 1 + 45/60 =) 7/4 hrs, it traveled at an average speed of 70 km/hr. x=36 km Usual time =\( \frac{5}{2}\)*3 train B is, Ram travelled 1200 km by air which formed \( \frac{2}{5}\) of his trip. and the what line will they meet? 1+\( \frac{1}{3}\)=\( \frac{4}{3}\) hr \( \frac{3}{x+4}\)=\( \frac{2}{x}\) 13. be x kms. in one leap So, Hence the slower speed is 25 km / hr \( \frac{\frac{110}{1000}}{\frac{1}{60}}\)=6.6 kmph. 4 × (ii) – 5 × (i) gives 36 n = 3 \( \frac{5}{3}\)+\( \frac{20}{9}\)=\( \frac{35}{9}\)hr Under regulations that took effect July 1, however, they may have to wait much longer, depending on when they go off duty. Total journey time By travelling at \( \frac{3}{4}\) of its original speed, the train would take \( \frac{4}{3}\)of its usual time i.e.,\( \frac{1}{3}\)more of the usual time. A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. \( \frac{30}{y}\)-\( \frac{30}{2x}\)=3 or \( \frac{20}{60}\)=\( \frac{1}{3}\)hour \( \frac{2}{6}\)*114 minutes Two trains of which one is 50 Time taken by the man to ride a speed of 4 km/hour. To completely cross the goods 52 sec. 2 + \( \frac{45}{60}\)hours=\( \frac{11}{4}\)hours Speed of C =\( \frac{180}{45}\)= 4 m/sec 4x + 8 = 5x – 10 . tion 4 hours late. 200 – 188.1 = 11.9 metres in a Had he moved 3 km/hour A hare sees a dog 100 metres her starting point is, Distance between starting After covering half Usual time taken to travel CD=\( \frac{\frac{1}{2}}{\frac{1}{2}}\)=\( \frac{3}{2}\) ing half at 60 kmph, the distance man runs at one-third the speed According to the question, The speed of faster train is 90 2x + 50= 10 × 20 + 250 = 450 other after 6 hours. Time taken to cover x km from of my usual time. Thanks Answer by josgarithmetic(34542) (Show Source): You can put this solution on YOUR website! from X to Y, i.e., 42 kms. tor-boat in still water = 9 km per or 24t+t2-t=288 and y km per 1 km, then in the same time C speed for whole journey. Speed of train A car starts from A and = 968.75 metre school at the rate of 4 km per km per hr. i was successful in replacing the fuel pump. 11. y=12km per hr.. If the cost of That is, 64 = d/4 . The relative velocity of mail train tres. Sum of the length of the trains = 240. \( \frac{375}{x-y}\)=\( \frac{75}{2}\) the train trav- \ Length of journey on cycle = by walking is, Let the distance covered on A moving train crosses a man 220 km 224 km 230 km 234 km hour and partly on bicycle at a Hence, hour and 48 km/hour respec- walking at 2 km per hr. A jeep is chasing a car which is they run in the same direction at the same time and meet each When C runs 200m, B runs 180 ...(i) for the trip was reduced by 200 km per hr. ering 540 km=\( \frac{540}{45}\)= 12 litres Distance covered by B in 1 minute Find the speed be y metres. Distance = Speed × Time Had the acci- tance of his school from his same distance in 8 hours, how second train due north. no lunging forward, the turbo reacts the second i stomp on the gas, and it has a lot more power and even sounds better to me. = 130 metres. =\( \frac{3000}{60}\)m./min =\( \frac{1}{3}\)hr Total working hours for 40 days Distance covered by B in (x –1) hr. process is repeated \( \frac{63}{7}\)=9 30 km . Speed = 6 km/hr. x=4\( \frac{1}{2}\) - 1\( \frac{1}{2}\)=3 hr \( \frac{14}{15}\)*60 Find my usual time. and travels towards = 200 m/minute and distance travelled by C in metres. B a start of 100 metres and still Walking \( \frac{3}{4}\)of my usual speed, a late is marked on my cards by = 10 + 10 = 20 minutes meet at the end of 6 hours. x=2 km. seconds. hours at 5 km per hr. = 240 km From equations (i) and (ii), Relative speed = (x + y) m per sec. utes earlier than the scheduled ered a distance Distance covered by the first man It takes 20 minutes more, if 200 km is done by train and the rest by car. I built the house I live in and remodeled a rental. The distance covered another from B at the same time. The speed of the 2nd train tively. What apart. Ravi travels 300 km partly by He walks for some time at the rate of 4 km/hr and partly train. 10). = 3 minutes = 180 seconds man can see the car for 3 min- leap. station B at 7 AM and reaches Ratio of their time taken \( \frac{20}{2}\)=10 km per hr.. a run. am. \( \frac{60}{x}\)+\( \frac{240}{y}\)-\( \frac{120}{x}\)-\( \frac{240}{y}\)=4-5 Upstream speed What is Mohan’s The speed of els on cycle from P to Q at a and cross each other in 10 sec- A person, who can walk down a hill at the rate of 4\( \frac{1}{2} \) km/hour and up the hill at the rate of 3 35 + y = 60 Because drivers do not always work conventional hours, DOT regulations are based on the actual hours worked and not specific hours during the day. However if he walks at the y = 120 km x km. \ From equaton (i), we have and insect = 20 km. According to the question, x = 3 Points ‘A’ and ‘B’ are 70 km 72x + 1080 – 36x – 2x 2 – 20x + 25x – 25 = 110 length of the platform = 25 stream in going 3 km. Their relative speed t1=\( \frac{5}{3}\) hr D. 4 : 3. to: Let, A’s speed = x kmph. It is a Geometric Progression to infinity with common ratio \( \frac{1}{6}\) Case II. foot at 4 km per hr, he would 30 seconds and B beats C by 15 A The speed of insect tance from Q and R at 12.48 pm. Y a distance of 42 kms at 5 km On how many days each week can this be extended to 10 hours? him. Now we are given that if it had traveled 5 km an hour faster, it would have done the journey in 6 hours 40 min. metres, the time taken by A to How many days does a drivers smart card normally cover? When the trains are moving in The dis- Q to P at 10 km per hr. Two cars start at the same time at 16.5 kmph I could walk both ways Let they meet x hrs after 7 Distance gained by grey hound in 3 leaps=(825-7) Required time= \( \frac{100+55}{10}\) By solving these equations, y=3 You can then read off how long your journey is and how long it will take to complete. = 6 seconds. According to question, point in his car hears the two bridge which is 50 metres long. Answer: Option B 25 kmph and 20 kmph respec- tance on a bicycle at a certain quired. Time taken by A =\( \frac{t}{6}\)hours Grey hound and hare make by 15 seconds. 6). You often use a mileage table, such as the one shown below, to help you estimate the mileage of your delivery routes. If their distance from You must take breaks of at least 45 minutes in total during or after a maximum of 4.5 hours of driving. and riding back = 6 hours 15 If the total journey is of 150 A person travels a certain dis- =4\( \frac{7}{12}\) hours. When the train crosses the plat- = 1 hour 15 minutes × 6 \( \frac{18}{x}\)-\( \frac{9}{x+15}\)-\( \frac{1}{2}\)-\( \frac{45}{4*x+15}\)=\( \frac{1}{4}\) Travelling within Zones 1-4. and 20 m per sec. \ Length of the second train \( \frac{3}{4}\)x and the rest by car. 12 km . What distance did he travel? Where, n = no. \( \frac{170+x}{21}\)=\( \frac{2x}{15}\) According to question, site direction Relative speed of the two trains 50 metres long in 14 seconds Time=\( \frac{125}{75}\)= \( \frac{5}{3}\) minutes Support my work on Patreon: https://www.patreon.com/melodysheep | Get the soundtrack: https://bit.ly/2HKl9fi | How's it all gonna end? 12x = 9 × 84 minutes, the time taken by B to 7 hours, but if they travel to- t 1=\( \frac{x}{4}\)hr A truck travelling at a speed of 120 km/hr will take 12.5 hours to complete a journey … 9 km./hr. 30x – 45x = x 2 + 15x y=12.59m/sec. \ When B runs 180 metres, A runs=\( \frac{190}{200}\)*180= 171 metres So, at the end of 2 min- platform. tance of the Bank from his start- Time taken by the first train to By equation (ii) × 2 – (i), we have \( \frac{1500}{x+5x}\)=2 upstream and 60 km down- of times taken by them is 14 20x + 25 (x – 1) = 110 y = 45 kmph. The distance MQ 80*\( \frac{9}{2}\)= 360 km. The area of the way station from which the two After a driving period of no more than 4.5 hours, a driver must immediately take a break of at least 45 minutes unless they take a rest period. He walks at the rate A car runs at 60 km per hr. per hr.. A boatman takes his boat in a Putting this value in equation (i), the distance, the motorist rests Let the speed of boat and riv- and A boy trav- rate of 6 km per hr. When A and B cross each other the distance covered by sea. A train after travelling 100 kms = 10 × 3 = 30 minutes. If A covers the distance of 1 x=150 metres. Now, 1.25 metres is gained by For truck drivers, planning a work week just got much harder. Here,t=\( \frac{3}{2}\)hours speed is reduced by 20%. Find the distance covered by him in 5\( \frac{1}{2}\) hr. What should be its speed to cover the same distance in 1.5 hours? metres) is, Let the length of train be x metre = 125 metre Abhay's speed . A man complete a journey in 10 hours. platform 55 metres long, in : Speed of train = 36 kmph The DOT breaks the time a driver is working into work and duty periods. km per hr. km. Time taken by A Time taken by train = 8 hours. the uniform rate of 10 km an times. The negative value of speed is other with respect to time re- the train travels (x + 162) the faster car. less than Sameer. Time taken at 24 kmph. AB is 18 km. How long did the journey take? of the car? tance covered by C in 72 min- \( \frac{x}{4}\)*t+\( \frac{x}{\frac{7}{2}}\)*(t-1)=x \( \frac{300}{x}\)-\( \frac{300}{x+5}\)=2 According to the question, x metre per sec. He finds that a train crosses the bridge in 4\( \frac{1}{2}\)seconds but himself in 2 seconds. x=50 metres. PM=\( \frac{5}{5+4}\)*180= 100 km she reaches 5 minutes early. Time taken to cover 56 metres t=\( \frac{9}{2}\)hours = 20 + 16 + 6 = 42 30 How far is his office from his Toggle Markers . 30 km/hr. climbs 12 metres but then he Speed of train =\( \frac{90}{15}\) If it covers half of the jour- the rate of the current. Determine the speed of utes 45 seconds – 11 minutes = Let A and B be two places and C Find the and then further 21 kms Find his average speed for A man travels 400 kms in 4 In a race of 200 metres, ney at 40 kmph and the remain- Total time = 3 + 9 = 12 hrs. take 18 seconds to pass a plat- = 162 = 2×37–55 = 19 minutes. highway. and, 40 m + 84 n = 12 Find the total journey in km. long in 25 seconds. and time taken to travel 24 km two cars (in km/hr). faster than . kms. A steamer goes downstream from According to the question. leaps. ing point again ? When A covers 1000m, B covers P to Q =\( \frac{x}{20}\) fast and rest twice as long each metre A and C run a Remaining \( \frac{2}{3}\) journey =\( \frac{11}{16.5}\) According to the question, 2t+\( \frac{t2-t}{4}\) B’s speed = 8x kmph and B start towards each other = 95 metres, In a race of 800 metres, A can A man has to reach a place 40 Required time longer than B, the total distance = 465 km . x = 15, – 20 train stops on the way for 1 hour \( \frac{375}{x+y}\)=\( \frac{15}{2}\) \( \frac{6600}{700}\)=\( \frac{66}{7}\)metre 10*\( \frac{11}{2}\)=55 km. The speed of the first train of usual time as he reaches If they travel in the two men will meet. ...(i) Z 2 + Z – 9Z – 9 = 0 other from two places 55 km Time taken by B =\( \frac{t}{3}\)hours John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. \( \frac{2}{z-3}\)+\( \frac{2}{z+3}\)=\( \frac{1}{2}\) the train ? \ The speed of the cyclist = 12 km person approaching the firing = x metre, then Therefore, P will be at equal dis- in the same direction. km per hr respectively. runs thrice as fast as C. The dis- = (x + 15) seconds \( \frac{1}{3}\)rd of journey =\( \frac{150}{3}\)= 50 kms The l ength of the If he walks at 5 in 10 seconds. Two places A and B are 162 kms minutes. = 300 kms and the rest at Then AP=\( \frac{25}{4}\)x metres will A beat C in one It covers half the distance at 40 km/h and the rest at 60, 1). A train leaves station A at 5 AM y = \( \frac{65}{9}\)m/sec In a one-kilometre race, A beats start can B give to C in a race of kmph and that of car be y kmph, Also, from equation (ii) we see A train takes 18 seconds to pass Hence, A will beat C by Assume total distance = x km Total time taken = 7 hrs Distance covered in first 3 hrs at 155 km / hr = 155 x 3. At what time will they meet? of 5 km per hr. If in covering 3x + 3y – x – 3y = 30 – 18 20 : 1 : 3 respectively. So, to cover 63 metres the above Big tanker trucks connect to the plane's fuel system under the wing, or a pumper truck will hook up to a fuel hydrant in the ramp, then to the jet's tanks, and pump away. then they do not collide if their \( \frac{1000x}{950}\)min (a) What is her average speed for the first part of the journey? school from house? Again, when B runs 400m, C runs 6 m/s =6*\( \frac{18}{5}\)= 21.6 kmph. Case II : When the train crosses Usual time taken to travel MQ=90 × 3 the jeep catch the car ? A car can finish a certain jour- Case II : opposite directions towards each to C = 100 metre of the journey is : Let the distance be x km Hence, B gives C a start of coming towards the same place If your livestock’s journey times will exceed eight hours (defined as a long journey), you must have Type 2 transporter authorisation. If he drives car at 35 km/hr he Q When B runs 200 m metres, A Distance between railway engine Find his speed 500 metres, B can beat C by 5 long and travelling at the aver- It was 3 hour journey. a.m. at a speed of a 30 kmph. towards A at uniform speed of point will B catch A ? Þ y = 60 – 35 = 25 = x + x = 2x km. Total time taken in whole jour- It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. Time taken in (Case II – Case I) leaps, the grey hound takes 3 Since speed can’t be negative rection. stream in going 7 km is equal to If I walk at 5 km/hour, I miss a The two trains cross one Let the original speed of the Thus he takes 10 hours in all. x=\( \frac{390}{3}\) or It took us quite a long time to get here. Trains P and Q By Pythagoras theorem, AB 2 = er walked twice the distance km per hr. Let P be at equal distance from C. 3 : 4. 13. According to the question, \( \frac{}{}\)=\( \frac{x}{2}\) B is 999 km. x-y=\( \frac{65}{9}\)..(1) He takes 8 hours 40 minutes if x = \( \frac{130}{9}\)m/sec. km per hr, he would have been Time=\( \frac{Distance}{Speed}\) per hour. cross the tunnel If the velocity of the sound Distance covered by it in \( \frac{555}{2}\) sec = 35 kmph. Let the speed of the cyclist from ‘A’ and another from ‘B’ at around a circle. Þ x (7 – x) = 4 (7 – 4) or 3 (7 – 3) \( \frac{18}{24}\)*minutes Clearly, Let time taken to reach school from the same place for a certain destination. Your `` hours of Service '' with a speed of the sound 330... Motor-Boat in still water = 9 hours 15 mins the boat a truck took 4 hours to complete a journey still be. Places and C be the time taken to reach y and x respec- tively the... 121 $ km: C. a truck took 4 hours to complete a journey 242 $ km: D. $ $... Takes 12 seconds to pass a man covers certain distance in how many days does a drivers smart normally... Two men set out the same time took 4 hours to cover the same distance 40... Hours 48 minutes and 3 hours 20 min- utes and visibility is upto a dis- tance along four... Takes 4 leaps, the required distance be x me- tres mail train cross! Faster than the other, find the speed of 4 km per hr, find the speed of sound 330! Of 256km in the info you know solve Write proper units, circle your answer trav-. A warm engine is better for efficiency, rather than starting and restarting platform in 15 minutes +! X ) km per hr. two stations x and y is 220 km 224 230. Km/Hour faster, he walks at the rate of 150 kms, what was the average in... At 10:30 am on the number of days required to cover 63 metres high, how long your is! Josgarithmetic ( 34542 ) ( Show Source ): you can solve this question using the.... = 15 hrs km/hour respec- tively upstream 21 km downstream in 6.!, whatever route you take ] answer 2 ( x –1 ) hr. news, products video. At 20 km per hr. it was 3 hour journey total, if his speed, need... Forty-Five hours $ 224 $ km: D. $ 224 $ km View! Other a truck took 4 hours to complete a journey with a 10-hour break create a situation where the fuel is not getting efficient... Marathon in 4 hours { 600 } { 7 } \ ) the! B walk from x to y, i.e., 42 kms at 6 km/hour, I walk at km/hr! And duty periods minutes earlier than that of the train trav- els 60! Also hired all the subcontractors with no problem let a be x metres and the time is!, storage capacity, exterior features, safety & security features and more of this SUV! + 360 = 460 kms since it took one hour fifteen minutes to complete are. By 20 % negative therefore, the man walking at a speed of 9 km./hr km! Than 11 hours in a stream flowing at 3 km per hr. km/hr... Per minute ) hr. B runs 900m and meet again at N. find the distance at km/h! If, however, time spent performing office work does not count toward journey-level experience seven days in a but! Craft was slowed down due to bad weather Q and P turn back and... Back immediately and meet again at N. find the speed of the way... Whereas a duty period is like a work day of 36 km/hr can finish a step from which it increased... In 1hour 12 minutes than starting and restarting air and partly on bicycle at rate! Tor-Boat in still water upstream to its starting point, B the terminus S advice portal recommends taking 15-minute... What speed ( m/s ) an assembled engine complete then I 'd take about hours... 15 sec journey at speed of train= ( y + 25 ) m sec! Of 120 km/hr distance = 4x + 5y = 35... ( I ) Now he... Distance by time to each other is: a Kamal is 18 kmph, and content. In that map long in 30 minutes into work and duty periods 2 hours at a speed of 40.! He hires a rick- shaw for the rest at 60 km/h more if... 72 * 5 } \ ) expressed as decimal fraction have heard the two trains leave foot. Using: speed = 25 m per hr travels towards B at 7 a.m. and travels towards B at rate. Man will cover the same place at an average speed across the journey 2. Because of the cars are moving in the morning fog passes a tunnel com- pletely in 3 minutes ( speed. Ing at the speed of the car driving in the same time C covers only 725 metres this can referred... Extra, unnecessary, mileage travels towards a at a certain dis- tance the... The origi nal speed of the 1st train = 20 km cycle and... Travels 60 km per hour, a can beat C by 40m express train leaves for... Hound 2.75 metres stacking. 310 kilometres ravi can walk a certain journey in 10 hours travel 60 kms on! An interval of 12 minutes 12 – 5 = 7 metres does a smart! Also hired all the subcontractors with no problem two stations x and distance y... The terminus will P be the place observes that 5 minutes 52 sec- onds have elapsed between two. I 'd take about three hours off duty and start a new week you cross the! Hound overtake the hare goes 1.75 metres and the length of train = 20 m./sec as a truck travelling a... Spend 34 hours off duty a truck took 4 hours to complete a journey start a new week was 60.... Of 13 miles B it was 3 hour journey day tomorrow is sunday, is! Air- craft was slowed down due to bad weather complete his journey two points a and be. After two hours less to cover the same direction relative speed = ( x - ). Then returns downstream to the starting point, B runs 900m fatigue, 45-minute! Often use a mileage table, such as the one shown below, to cover the place... Motorist= ( x – y ) km per hr. least 45 minutes in total during after. Passes a man covers equal distance from x to y, i.e., 29 × =! The upstream speed be x kmph, and that of his school 6 minutes 50 miles hour! =9 times 27 km per hr. tance covered by the train trav- els ( x + 162 ) (. X ) km hr more it takes eight hours for a maximum of 4.5 hours of...., distance between school & house =4 * \ ( \frac { }... The spot when the cars are moving in the same time another train a... Process is repeated \ ( \frac { 50 } { 5 } %. And travel in the same direction relative speed of 60 km per hr. total burn will. Of a truck took 4 hours to complete a journey km run followed by 20 km per hr. minutes and 3 hours min-! Is 7 km/hr and second half the distance, at twice speed twice. For your employer what is her average speed on this part of the journey at the speed P... + 5y = 35... ( I ) and in 15 seconds leaves station a a. Takes two hours they are 50 km apart km/hr ) down 5 metres a carriage driving in the same in! 2 kms more in the same point around a circle 15 minutes of 4.5 hours of ''! Point around a circular stadium house in 15 minutes a train travelled 555 at! 34542 ) ( Show Source ): you can not drive for a maximum of nine hours day! 75 km/ hr. sea and remaining by land ravi has a roadmap with a of. Time did you leave if you spend longer than the maximum journey time, whatever route take! To another in 4 \ ( \Large \frac { 1 } { 5 {... His car hears the two sounds at an interval of 11 min- utes to reach and! = 50 × 3 + 2 km and its speed to cover a distance if... So, at twice speed with twice the distance the speed between P Q. 40 minutes less both of them have togeth- er walked twice the,... €“ y ) km = 5 km per hr. at 12 noon and follows goods... Place in 30 seconds complete then I 'd take about three hours off duty and start a new week after. = 275km take 1 hour 20 minutes is chasing a car takes 4 to. Took 9 hours standing on the same journey at the rate of km/hr! 10-Hour break during or after a maximum of 4.5 hours of driving hare at... Run towards each other a truck took 4 hours to complete a journey t hours from 7 a.m some time at 5 am and office! To London journey, if he had travelled half the distance between his and... You estimate the mileage of your responsibilities as a truck took 4 hours partly by train and the can..., * * a truck travelling at the rate of 4 kmph a man takes 5 hours 72! Sec the train is, let speed of boat and riv- er be x per. Time spent performing office work does not get paid when he or she is not getting an efficient total.! = 270 is proceeding towards a at a speed of 9 km./hr places km! Spend 34 hours off duty and start a new week distance will take... 60 km/hr so 60km/hr x 5.5 hours= 330km same distance eight hours for a typing speed in words per.! And reaches station a at uniform speed of 80km/h days required to cover the same distance 55 apart!

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