Time Speed and Distance Exercise

Abhishek Jain

1. Raja has to leave office exactly after 20 minutes to catch a train which leaves station 6.40 p.m. and its 5.45 p.m. now. How much time does it take to travel from office the station? Ans: 35 minutes

2. Balu started in a car from Cochin to Trivandrum at 11 a.m. He travelled at 60 km per hour and covered half the distance in two hours At what uniform speed should he travel to reach Trivandrum at 4.00 p.m.? Ans: 40 km/hour

3. The charges of hired car are Rs. 3 per km for the first 60 km. Rs. 5 per km for the next 60 km and Rs. 10 per km for the further journey. If the balance amount left over with Atul is less than what he paid towards the charges of the hired car for travelling 200 km. how much money did he have initially with him? Ans: Rs. 1216

4. A travels a certain distance at a speed of x km per hour and an equal distance at the speed of y km per hour. Then the average speed of A for the whole journey (in km) per hour is Ans: 2xy/(x+y)

5. I ascend a mountain with a speed of 3 km per hour. Then I immediately return from the summit and run downwards with

a speed of 6 km per hour. Then my average speed for the round trip is Ans: 4 km/hour

6. A and B are walking in the same direction. A who is an ahead walks at the rate of 3.5km an hour while B walks at the rate of 4 km per hour. The distance between then is 6 km. The B overtakes A in Ans: 12 hours

7. A man riding a cycle at 12 km per hour can reach a village in 4.5 hours. If he is delayed by 1.5 hour at the start, then in order to reach his destination in time, he should ride with a speed of Ans: 18 km/hour

8. A boy goes to school with a speed of 3 km/hour and returns with a speed of 2 km/hour. If he takes 5 hours in all, then the distance (in km/hour) between the village and the school is: Ans: 6

9. A boy walks to school at the rate of 3 km per hour and reaches school at 7.35 a.m. Then he walks at 5 km per hour and reaches at 7.25 a.m. If his school time is 7.30 a.m. how far is his school from his house? Ans: 1.25 km

10. A car is travelling is at the rate of 50km per hour whereas train is moving at 20 meters per second. Their respective

speeds are in the ratio Ans: 25:36

11. A thief steals a scooter and drives of 60 km per hour. The policeman discovers the theft after 15 minutes and start chasing him at the rate of 75 km per hour his motor-cycle. After what time the thief caught by the police man? Ans: one hour

12. A car covers a distance of 690 km in 30 h. What is the average speed of the car? Ans: 23 km/h

13. A bus is running with a uniform speed of 37 km/h. What distance will be covered by bus in 8 h? Ans: 296 km

14. A person riding a bike crosses a bridge with a speed of 54 km/h. What is the length of the bridge if he takes 4 min to cross the bridge? Ans: 3600 m

15. A man covered a distance of 12 km in 90 min bycycle. How much distance will he cover in 3 h if he rides the cycle at a uniform speed? Ans: 24 km

16. A man completes 30 km of a journey at 6 km/h and the remaining 40 km of the journey in 5 h. Find the average speed for the whole journey Ans: 7 km/h

17. A certain distance is covered at a certain speed. If half of the distance is covered in double time, the ratio of the two speeds is Ans: 4:1

18. Moving of its usual speed a train is 10 min late. Find its usual time to cover the journey Ans: 60 min

19. A car covers a distance from town A to town B at the speed of 58 km/h and covers the distance from town B to town A at the speed of 52 km/h. What is the approximate average speed of the car? Ans: 55 km/h

20. A car reached Raipur from sonagarh in 35 min with an average speed of 69 km/h. If the average speed is increased by 36 km/h, how long will it take to cover the same distance? Ans: 23 min

21. A student walks from his house at 2.5 km/h and reaches his school late by 6 min. Next day, he increases his speed by 1 km/h and reaches 6 min before school time. How far is the

school from his house? Ans: km

22. John started from A to B and vinod from B to A. If the distance between A and B is 125 km and they meet at 75 km from A. What is the ratio of Johns speed to that of vinods speed? Ans: 3:2

23. A man covers half on his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed Ans: 4 km/h

24. The speeds of A and B are in the ratio of 3:4. A takes 20 min more than the time taken by B to reach a destination, in what time does A reach the destination? Ans: 1.33 h

25. A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 56 min will be covered by A in Ans: 9.33 min

26. The ratio of speeds of a train and a car is 16:15 respectively and a bus covered a distance of 480 km in 8 h. The speed of the bus in of the speed of train. What distance will be covered by car in 6 h? Ans: 450 km

27. The ratio between the speeds of two buses is 5:3. If the 1st bus runs 400 km in 8 h, then find the speed of the 2nd bus. Ans: 30 km/h

28. If sohail walks from his home to office at 16 km/h, he is late by 5min. If he walks at 20 km/h, he reaches 10 min before the office time. Find the distance of his office from his house Ans: 20 km

29. A car covers a distance of 200 km in 2 h 40 min whereas a jeep covers the same distance in 2 h. What is the ratio of their speeds? Ans: 3:4

30. A person goes from one point to another point with a speed of 5 km/h and comes back to starting point with a speed for 3 km/h. Find the average speed for the whole journey. Ans: 3.75 km/h

31. A bus travels at the rate of 54 km/h without stoppages and it travels at 45 km/h with stoppages. How many minutes does the bus stop on an average per hour? Ans: 10 min

32. A car travels a distance of 75 km at the speed of 25 km/h. It covers the next 25 km of its journey at the speed of 5 km/h and

the last 50 km of its journey at the speed of 25km/h. What is the average speed of the car? Ans: 15 km/h

33. A car runs at the speed of 40 km/h when not serviced and runs at 65 km/h when serviced. After servicing the car covers a certain distance in 5 h. How much approximate time will the car take to cover the same distance when not serviced? Ans: 8 h

34. An express train travelled at an average speed of 100 km/h, stopping for 3 min after every 75 km. A local train travelled at a speed of 50 km/h, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometers did the local train travel in the time in which the express train travel 600 km? Ans: 307.5 km

35. If you travel 39 km at a speed of 26 km/h, another 39 km at a speed of 39 km/h and again 39 km at a speed of 52 km/h. What is your average speed for the entire journey? Ans: 37 km/h

36. A and B are two stations 1000 km apart. A train starts from A and moves towards B at 40 km/h. Another train starts from B at the same time and moves towards A at 60 km/h. How far from A will they cross each other? Ans: 400 km

37. X and Y start walking towards each other at 8 am at the speeds of 3 km/h and 4 km/h, respectively. They were initially 17.5 km apart. At what time do they meet? Ans: 10.30 am

38. A train leaves Manipur at 6 am and reaches Dispur at 10 am. Another train leaves Dispur at 8 am and reaches Manipur at 11:30 am. At what time do the two trains cross trains cross each other? Ans: 8:56 am

39. The average speed of a car is 75 km/h. The driver first decreases its average speed by 40% and then increases it by 50%. What is the new average speed now? Ans: 67.5 km

40. A car runs at the speed of 50 km/h when not serviced and runs at 60 km/h, when serviced. After servicing, the car covers a certain distance in 6 h. How much time will the car take to cover the same distance when not serviced? Ans: 7.2 h

41. A car driver covers a distance between two cities at a speed is 60 km/h and on the return his speed is 40 km/h. He goes again from the 1st to the 2nd city at twice that original speed and returns at half the original return speed. Find his average speed for the entire journey. Ans: 40 km/h

42. The distance between two stations X and Y is 450 km. A train L starts at 6 pm from x and moves towards y at an average speed of 60 km/h. Another train M starts from y at 5:20 pm and moves towards x at an average speed of 80 km/h. How far from x will the two trains meet and at what time? Ans: 170 km, 8:50 pm

43. Two cars A and B are running towards each other from two difference places 88 km apart. If the ration of the speeds of the cars A and B is 5:6 and the speed of the car B is 90 km/h, after what time will they meet each other? Ans: 32 min

44. If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds, then the speed of the train is Ans: 72 km/h

45. A train 150 m long is running at a speed 90 kmph. Time taken by the train to cross a tree is Ans: 6 sec

46. A 100 m long train crosses a stationary man in 10 seconds. What is the speed of the train? Ans: 36 km/h

47. Two trains A and B, travelling in opposite directions, cross each other in six seconds. The speed of train A is 126 km/h, while that of train B is 90 km/h. If the length train A is 160

metres, what is the length of train B? Ans: 200 m

48. A train crosses a stationary person in 3 seconds while it takes 10 seconds to cross a platform, travelling at same speed. If the length of the platform is 210 meters, what is the length of the train? Ans: 90 m

49. A 225 m long train crosses another 150 m long train in 12.5 sec. If one of the trains travels @ 72 km/h, what is the speed of the other? Ans: 36 km/h

50. What is the sped of a train which overtakes a man walking at a speed of 5 km/h in 30 seconds, if the train is 274 metres long? Ans: 37.88 km/h

51. Two trains (X, Y) start from A and B respectively, towards each other. After they meet at point C, the train X takes two hours to reach B while the train Y takes 4.5 hour to reach A. If the distance between places A and B is 450 kms, how far should C be from A? Ans: 270 km

52. 150 m long train takes 10 s to pass a man who is going in the same direction at 2 km/h. What is the speed of the train in km/h? Ans: 56

53. A train starts from station X at the rate of 60 km/h and reaches station Y in 45 minutes. If the speed is reduced by 6 km/h. how much more time will the train take to return from station Y to station X? Ans: 5 min

54. A train takes 18 seconds to pass completely throught a station 162 m long and 15 seconds through another station 120 m long. The length of the train is Ans: 90 m

55. A train 100 metre long completely passes a man walking in the same direction at 6 km/h in 5 seconds and a car travelling in the same direction in 6 seconds. At what speed was the car travelling? Ans: 18 km/h

56. How many seconds will a 500 metres long train take to cross a man walking with a speed of 3 km/h in the direction of the moving train if the speed of the train is 63 km/h? Ans: 30

57. A train runs at the rate of 120 km/h. The speed in metres per second is Ans: 33.33

58. A train running at the speed of 72 km/h crosses a 260 metres long platform in 23 seconds. What is the length of the train in metres? Ans: 200

59. Train A leaves Mumbai Central station for Lucknow at 11 a.m. running at the speed of 60 km/h. Train B leaves Mumbai Central station for Lucknow by the same route at 2 p.m. on the same day running at the speed of 72 km/h. At what time will the two trains meet each other? Ans: 5 am on the next day

60. A train running at speed of 120 km/h crosses a signal post in 15 seconds. What is the length of the train in metres? Ans: 500

61. Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/h and 40 km/h respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is Ans: 900 km

62. A train running at of its own speed reached a place in 22 hours. How much time could be saved if the train ran at its own

speed? Ans: 8 h

63. A train is 125 m long. If the train takes 30 seconds to cross a tree by the railway line, then the speed of the train is Ans: 15 km/h

64. A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is Ans: 200 m

65. A train 800 metres long is running at the speed of 78 km/h. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is Ans: 500

66. Two trains one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km/h and the other at 67 km/h. How long will they take to cross each other? Ans: 7.5 s

67. Two trains start at the same time, one from New Delhi to Agra, the other from Agra to New Delhi, if they arrive at their respective destinations in one hour and four hours respectively after passing each other, how much faster is one train running

than the other? Ans: 2 times

68. A and B are two stations 500 km apart. A train starts from A and moves towards B at the rate of 20 km/h. Another train starts from B at the same time and moves towards A at the rate of 30 km/h. How far from A will they cross each other? Ans: 200 m

69. A passenger train, moving at the rate of 90 km/h overtakes a goods train, 2 times as long and moving on parallel lines at the rate of 50 km/h and passes it completely in 54 seconds. How long would the passenger train take to pass completely through a station 400 meters in length? Ans: 24 s

70. Two trains for Bombay leave Delhi at 6 am and 6.45 am and travel at 100 km/h and 136 km/h respectively. How many kilometers from Delhi will the two trains be together? Ans: 283.33 km

71. Two trains, Calcutta Mail and Bombay Mail, start at the same time from stations Calcutta and Bombay respectively towards each other. After passing each other, they take 12 hours and 3 hours to reach Bombay and Calcutta respectively. If the Calcutta Mail is moving at the speed of 48 km/h, the speed of the Bombay Mail is Ans: 96 km/h

72. Without stoppage, a train travels a certain distance with an average speed of 60 km/h, and with stoppage, it covers the same distance with an average speed of 40 km/h. On an average, how many minutes per hour does the train stop during the journey? Ans: 20 min/h

73. A railway passenger counts the telegraphs poles on the rail as he passes them. The telegraph poles are at a distance of 50 metres. What will be his count in 4 hours, if the speed of the train is 45 km/h? Ans: 3600

74. Two trains A and B start simultaneously in the opposite directions from two points A and B and arrive at their destinations in 9 and 4 hours respectively after their meeting each other. At what rate does the second train B travel if the first train travels at 80 km/h? Ans: 120 km/h

75. Two trains from Howrah leave Muzaffarpur at 8.30 am and 9.00 am respectively and travel at 60 km/h and 70 km/h respectively. How many kilometers from Muzaffarpur will the two trains meet? Ans: 180 km

Directions for (Q. No 76 & 77): Answer the following questions on the basis of the information given below: (i) Trains A and B travelling on the same route heading towards the same train destination. Train B has already covered a distance of 220 kms before the train started

(ii) The two trains meet each other after 11 hours after the start of train A (iii) Had the trains been travelling towards each other, (from a distance of 220 km) they would have met after one hour

76. What is the speed of train B in km/h? Ans: 100

77. What is the speed of train A in km/h? Ans: 120

78. A train meets an accident after moving 30 km. Its speed then comes down to th of the original one and consequently runs 45 mins late. Had the accident taken place 18 km farther away, it would have been 36 min late. Find the original speed of the train and the distance between the two stations Ans: 30 km/h, 120 km

Directions for (Q. No 79 & 80): Read the following and answer the questions that follow. The Kalinga Express started from Patna to Tata at 7 pm at a speed of 60 km/h. Another train, the Rajadhani Express, started form Tata to Patna at 4 am next morning at a speed of 90 km/h. The distance between Patna to Tata is 800 km

79. How far from Tata will the two trains meet? Ans: 156 km

80. At what time will the two trains meet? Ans: 5:44 am

81. A train 600 m long crosses a pole in 12 s. What is the speed of the train in km/h? Ans: 180 km/h

82. A train moving with a speed of 25 m/s crosses a standing man in 16 s. What is the length of the train? Ans: 400 m

83. A train 130 m long passes a bridge in 20 s moving with a speed of 90 km/h. Find the length of the bridge Ans: 370 m

84. A train 250 m long crosses a platform of equal length in 50 s. Find the speed of the train Ans: 10 m/s

85. A train speeds past a pole is 10 s and speeds past a platform of 300 m in 25 s. Its length in metres is Ans: 200 m

86. A train 100 m long completely passes a man walking in the same direction at 2 km/h in 9 s and a car travelling in opposite

direction in 3 s. At what speed was the car travelling? Ans: 78 km/h

87. Two trains of equal length are running on parallel lines in the same direction at 45 km/h and 35 km/h. The faster train passes the slower train in 27 s. The length of each train is Ans: 300 m

88. A man in a train notices that he can count 21 telephone posts in 2 min. If they are known to be 50 m apart, then at what speed is the train travelling? Ans: 30 km/h

89. A train of length 150 m takes 40 s to cross a tunnel of length 300 m. The speed of the train is Ans: 40.5 km/h

90. If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/hour, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is Ans: 19

91. A train overtakes two persons who are walking in the same direction in which the train is running, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds

respectively. The length of the train (in metres) Ans: 50

92. Two trains of length 70 m and 80 m are running at speeds of 68 km/hr and 40 km/hr respectively on parallel tracks in opposite directions. In how many seconds will they pass each other? Ans: 5

93. A man rows 6 km/h in still water. If the river is running at 3 km/h, it takes him 45 minutes to row to place and back. How far is the place? Ans: 1. 6875 km

94. A boat goes 15 km upstream in 80 minutes. The speed of the stream is 5 km/h. The speed of boat in still water is Ans: 16.25 km/h

95. In a stream, B lies in between A and C such that it is equidistant from both A and C. A boat can go from A to B and back in 6 h 30 minutes while it goes from A to C in 9 h. How long would it take to go from C to A? Ans: 4 h

96. In a stream that is running at 2 km/h, a man goes 10 km upstream and comes back to the starting point in 55 min. Find the speed of the man in still water Ans: 22 km/h

97. A motorcycle whose speed in still water is 15 km/h goes 30 km downstream and comes back in a total 4 hours 30 min. Determine the speed of the stream Ans: 5 km/h

98. Two swimmers, at opposite ends of a 90-foot pool, start to swim the length of the pool, one at the rate of 3 feet per second, the other at 2 feet per second. They swim back and forth for 12 minutes. Allowing no loss of time at the turns, find the number of times they pass each other Ans: 20

99. Two ports A and B are 300 km apart. Two ships leave A for B such that the second leaves 8 hours after the first. The ships arrive at B simultaneously. Find the time the slower ship spent on the trip if the speed of one of them is 10 km/h higher than of the other Ans: 20 h

100. In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is Ans: 8

101. A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is Ans: 2.5 km/hr

102. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current Ans: 1.5

103. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water? Ans: 6 km/hr

104. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water? Ans: 1 hr 15 min

105. A man can row three-quarters of a kilometer against the stream in 11.25 minutes. The speed (in km/hr) of the man in still water is Ans: 5

106. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is Ans: 3:1

107. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? Ans: cannot be determined

108. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is Ans: 13 km/hr

109. A mans speed with the current in 15 km/hr and the speed of the current is 2.5 km/hr. The mans speed against the current is Ans: 10 km/h

110. If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man rate along the current is: Ans: 6.5 kmph

111. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream Ans: 4 hours

112. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is Ans: 24 hours

113. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is Ans: 3.6 km

114. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? Ans: 2.4 km

115. A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph. What is the distance between A and B? Ans: 180 km

116. A man can row 9.33 kmph in still water and finds that it takes him thrice as must time to row up than as to row down the same distance in the river. The speed of the current is Ans: 4.66 km/hr

117. A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? Ans: 15 kmph

118. A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is Ans: 5

119. The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is Ans: 3 km/hr

120. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is Ans: 2 mph

121. A man rows to a place 48 km distance in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is Ans: 1 km/hr

122. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream

in 6.5 hours. The velocity of the current is Ans: 2 mph

123. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour? Ans: 2.66

124. A man can row upstream at 7 km/h and downstream at 11 km/h. What is the mans rate in still water? Ans: 9 km/h

125. A man can row up stream at 4 km/hr and downstream at 7 km/h. What is the rate of the current? Ans: 1.5 km/h

126. A man rows 25 km downstream and 20 km upstream taking 5 h each time. What is the velocity of the current? Ans: 0.5 km/h

127. A man can row 9 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of the stream Ans: 3 km/h