Time and Distance
Formula: - Distance = Speed * Time
Time = Distance / Speed
Speed = Distance / Time
Average Speed: - If a certain distance at Two different speed i.e., if a distance x is covered at a km/hr and the same
distance is covered at b km/hr, then the average speed of the journey is calculated as 2ab / (a+b) Km/hr.
1. If the two bodies are moving in the same direction at a km/hr and b km/hr, such that a > b, then their relative
speed = (a-b) km/hr
Ex. If two cars are moving towards South with the speeds 20 km/hr and 35 km/hr respectively, find their relative
speed?
2. If two bodies are moving in the opposite directions at a km/hr and b km/hr, then their relative speed = (a+b)
Km/hr.
Ex. If two buses are moving in the opposite directions, their speed having 40 km/hr and 25 km/hr respectively, find
their relative speed?
3. It two bodies are moving in the same direction with different velocities, initiating earlier, then the distance
covered by both the bodies at the point of overtake is same for both the bodies.
Ex. A man leaves a town at 8 am. on his bicycle moving at 10 km/hr. Another man leaves the same town at 9 am. on
his scooter moving at 30 km/hr. At what time does he overtake the man on his bicycle?
4. If two bodies initiate at two opposite points and start moving towards each other, then sum of the distance covered
by them till their crossing point is the total distance between the two extreme points.
Ex. If two cars A and B move towards each other, where car A starts at 9 am. and Car B at 10 am. The speeds of the
Car A and Car B are 40 km/hr and 50 km/hr respectively. What distance does car travel when the two cars meet, if
the initial distance between A and B is 400 km?
5. If an object changes its speed in the ratio m: n, then the ratio of times taken becomes n: m.
Ex. The ratio between the rates of walking of A and B is 2:3. If the time taken by B to cover a distance is 24
minutes, the time taken by A to cover the same distance would be?
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1. A man covers a certain distance at 90 km/hr. and returns back to the starting point at 60 km/hr. His average speed
during the whole journey is
(A) 60 km/hr (B) 65 km/hr (C) 72 km/hr (D) 75 km/hr (E) 78 km/hr
2. Speed of 63 km/hr can be expressed in m/sec as
(A) 16 m/sec (B) 17 m/sec (C) 17.5 m/sec (D) 18.5 m/sec (E) 19 m/sec
3. Speed of 18 m/sec can be expressed into km/hr as
(A) 55 km/hr (B) 62 km/hr (C) 64.8 km/hr (D) 65.2 km/hr (E) 67.8 km/hr
4. Column A: The time required to travel d miles at 5 miles per hour
Column B: The time required to travel 2d miles at 25 miles per hour.
5. If a car travels 1/100 of a kilometer each second, how many meters does it travel per half an hour?
(A) 12000 (B) 15000 (C) 16000 (D) 18000 (E) 20000
6. A man goes up hill with an average speed of 20 km/hr and comes down with an average speed of 30 km/hr. The
distance travelled in both the cases being the same, the average speed for the entire journey is
(A) 18 km/hr (B) 22 km/hr (C) 24 km/hr (D) 26 km/hr (E) 30 km/hr
7. If a man running at 20 km/hr crosses a bridge in 12 minutes, the length of the bridge is
(A) 1000 m (B) 2500 m (C) 3575 m (D) 4000 m (E) 4500 m
8. A man travels first 80 km at 20 km/hr, next 30 km at 15 km/hr and then 80 km at 20 km/hr. His average speed for
the whole journey (in km/hr) is
(A) 20 (B) 22 (C) 17 (D) 19 (E) 25
9. A man walks at the rate of 4 km/hr for 5 hour and at 3 km/hr for 10 hours. The average speed of the man (in
km/hr) is
1 1 2 3
(A) 3 (B) 3 (C) 3 (D) 3 (E) 3
3 2 3 4
10. Distance covered in 2 hours 15 min at 4 kmph. Time taken to cover it at 18 kmph is
(A) 15 min (B) 25 min (C) 30 min (D) 45 min (E) 50 min
11. A car covers four successive 4 km distances at speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively.
Its average speed over total distance is
(A) 10 kmph (B) 20 kmph (C) 25 kmph (D) 30 kmph (E) 35 kmph
12. Jonny travels from his home to his class at an average speed of 8 miles per hour and then travels from his class
to his home along the same route at an average speed of 4 miles per hour. If his whole journey took 3 hours, the
distance between his home and his class is
(A) 3 (B) 5 (C) 6 (D) 8 (E) 4
13. A train 200 m long is going with a speed of 60 kmph. In what time will it pass electricity pole?
(A) 8 sec (B) 10 sec (C) 12 sec (D) 13 sec (E) 15 sec
14. First 150 miles of his trip, john drove at 50 mile per hour, and then due to traffic, he drove at only 20 miles per
hour for the next 120 miles. His average speed, in miles per hour, for the entire trip is
(A) 20 (B) 28 (C) 30 (D) 32 (E) 35
15. In A hours and B minutes, a man travel C miles. The man’s speed in miles per hours?
𝑐 𝐶 60𝐶 60 60
(A) (B) (C) (D) (E)
60+𝐵 𝐴+𝐵 60𝐴+𝐵 60+𝐵 60𝐶
16. Two trains start at the same point and travel in opposite direction. If one train travels at 30 miles per hour and the
other at 50 miles per hour, the time lapsed before they are 240 miles apart is
(A) 1 hour (B) 1.5 hour (C) 0.5 hour (D) 2 hours (E) 3 hours
17. A car covers a distance in 50 minutes. If it runs at 48 kmph on an average speed, the speed at which the car
should run to reduce the time of journey to 40 minutes will be?
(A) 50 kmph (B) 55 kmph (C) 60 kmph (D) 70 kmph (E) 75 kmph
18. A car travels 70 kilometers in one hour before some fault happens, then it travels for 120 kilometers at 30
kilometers per hour, for the entire trip average speed is
(A) 33 (B) 36 (C) 38 (D) 40 (E) 42
4
19. If a man travels x miles per hour for 5 hours and then travels x miles per hour every hour thereafter, the miles
3
he drive in 20 hours will be
25
(A) 10x (B) 25x (C) x (D) 12x (E) 26x
2
20. A motor travels 100 miles at rate of 40 miles per hour. If it returns the same distance at a rate of 50 miles per
hour, the average speed for the entire trip, in miles per hour is
200 50 400
(A) (B) 40 (C) (D) (E) 55
3 9 9
21. A cyclist travels 30 miles at a speed of 15 miles per hour. If he returns along the same path and the entire trip
takes 2.5 hours. Then the speed at which he has to return will be
(A) 15 mph (B) 25 mph (C) 40 mph (D) 55 mph (E) 60 mph
22. Column A: Tom takes 2 hrs at a speed of 40 miles per hours to drive from home to the class.
Column B: On the other hand it takes 1.5 hours at an average speed 45 miles per hour for Tom to drive from his
Home to the park.
23. A boy has to cover a distance of c km. at a speed of a kmph. But due to rain his speed is reduced by b kmph
(a>b). If he takes d hours to cover the distance, then
𝑐 𝑐 1 1 𝑐 1
(A) =a-b (B) d=a+b (C) d=a-b (D) = + (E) =
𝑑 𝑑 𝑎 𝑏 𝑑 𝑎−𝑏
24. Rima reaches school 10 minutes late at the speed of 12 kmph. Next time she covers the distance at 15 kmph and
reaches the school 10 minutes earlier that the school time. The distance of her school from her house is (in Km)
(A) 12 (B) 15 (C) 17 (D) 20 (E) 23
26. A car covers a distance in 36 minutes. It runs at 50 kmph on an average. The speed at which the car must run to
reduce the time of journey by 6 minutes will be?
(A) 30 kmph (B) 42.86 kmph (C) 55 kmph (D) 60 kmph (E) 75 kmph
27. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph for how many
minutes does the stop per hour?
(A) 12 (B) 10 (C) 15 (D) 16 (E) 8
28. Two men starting from the same place walk at the rate of 4 kmph and 5.5 kmph respectively. What time will
they take to be 5.25 km apart if they walk in the same direction?
(A) 2 hour (B) 3 hour (C) 3.5 hour (D) 3.67 hours (E) 4.5 hours
29. Two buses travel to a place at 45 kmph and 60 kmph respectively. If the second bus takes 5.5 hours less than the
first for the journey, the length of the journey is?
(A) 900 km (B) 945 km (C) 950 km (D) 990 km (E) 1350 km
30. George starts jogging from point X to point Y. Half an hour later, his friend Jack who jogs 1 mile per hour
slower than twice George’s rate starts from the same point and follows the same path. If Jack overtakes George in 2
hours, how many miles will Jack have covered?
11 10 20
(A) (B) (C) 4 (D) 6 (E)
5 3 3
31. Two cars start moving from the same at the same time in the opposite direction. If the rate of one car is 20 mph
faster than the other and after 3 hours they are 300 miles apart, what is the rate of the faster car?
(A) 40 m/hour (B) 50 m/hour (C) 55 m/hour (D) 60 m/hours (E) 65 m/hours
32. A car travelled from city P to city R in 30 minutes. The first half of the distance was covered at 50 miles per
hour, and the second half was covered at 60 miles per hour. What was the overall speed of the car?
200 400 500 600 700
(A) (B) (C) (D) (E) .
11 11 11 11 11
33. Robert leaves from point A to point B which is 200 miles away. One hour later, Craig leaves from point B for
point A. if Robert drives at 60 mph and Craig drives at 40 mph, how many miles will Craig have driven when they
cross each other?
(A) 56 (B) 58 (C) 60 (D) 65 (E) 80
34. A leaves the town on his bicycle 15 kmph at 9 a.m. Two hours later, B leaves the same town at 18 kmph in the
same direction. At what time does B pass A?
(A) 5 p.m. (B) 6 p.m. (C) 8 p.m. (D) 7 p.m. (E) 3 p.m.
35. A is twice fast as B and B is thrice fast as C is. The journey covered by C in 42 mins. The journey will be
covered by A in
(A) 5 mins (B) 6 mins (C) 6.5 mins (D) 7 mins (E) 7.5 mins
36. If a car runs at 30 kmph, it reaches it destination late by 15 minutes, but if it runs at 40 kmph. It is late by 5
minutes only. The correct time for the car to complete its journey is
(A) 15 min (B) 18 min (C) 19 min (D) 23 min (E) 25 min
37. A man covers a certain distance on his vehicle. If he moves 5 kmph faster, he have taken 30 minutes less. If he
moves 4 kmph slower, he would have taken 30 minutes more. The distance (in km) is
(A) 150 (B) 160 (C) 175 (D) 180 (E) 200
38. Two cars travel away from each other in opposite direction at 26 miles per hour and 45 miles per hour
respectively. If the first car travels for 30 minutes and the second car for 40 minutes. The distance (in miles)
between them at the end of their trips is
(A) 25 (B) 28 (C) 35 (D) 40 (E) 43
39. Two trains starts from stations A and B and travel towards each other at speed of 50 kmph and 70 kmph
respectively. At the time of their meeting the second train has travelled 100 km more than the first. The distance
between A and B is
(A) 600 km (B) 650 km (C) 700 km (D) 550 km (E) 500 km
40. In covering a certain distance, the speeds of A and B are in the ratio of 5:6. A takes 50 minutes, more than B to
reach the destination. The time taken in hours by A to reach the destination is
(A) 3.5 (B) 4 (C) 4.33 (D) 5 (E) 5.25
41. A man drives 150 km from A to B in 3 hours 20 minutes. He comes back from B to A in 4 hour 10 minutes.
Then, average speed from A to B exceeds the average speed for the entire trip by
A) 4 km/h (B) 4.5 km/h (C) 5 km/h (D) 3 km/h (E) 7 km/h
42. The ratio between the speeds of A and B is 3:4 and therefore A takes 30 minutes more than the time taken by B
to reach a destination. If A has walked at double the speed, he would have covered the distance in
(A) 40 min (B) 55 min (C) 60 min (D) 70 min (E) 75 min
43. The A leaves Agra at 5 a.m. and reaches Delhi at 9 a.m. Another train B leaves Delhi at 7 a.m. and reaches Agra
of 10:30 a.m. The two train cross one another at
(A) 7:30 a.m. (B) 7:56 a.m. (C) 8:15 a.m. (D) 8:36 a.m. (E) 9:16 a.m.
44. At 9.00 am train T left a train station and 2 hours later train S left the same station on a parallel track. If train T
average 60 kilometer/hrs and train S average is 75 km/hrs until S overtake T, at what time did S overtake T?
(A) 2.00 p.m. (B) 5.00 p.m. (C) 6.00 p.m. (D) 7.00 p.m. (E) 9.00 p.m.
45. A point on the edge of a fan blade that is rotating in a plane is 10 centimeter from the centre of the fan. What is
the distance travelled, in centimeter, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per
minute?
(A) 750 𝜋 (B) 1500 𝜋 (C) 1875 𝜋 (D) 3000 𝜋 (E) 7500 𝜋
46. During a trip, Francine travelled x percent of the total distance at an average speed of 40 miles per hour and the
rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francines average speed for the
entire trip?
180−𝑥 𝑥+60 300−𝑥 600 12000
(A) (B) (C) (D) (E) .
2 4 5 115−𝑥 𝑥+200
46. On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline,
rounded to the nearest gallon. The actual number of miles per gallon that Cindys car got on this trip must have been
between
290 290 295 285 285 295 285 295 295 285
(A) And (B) and (C) and (D) and (E) and
12.5 11.5 12 11.5 12 12 12 11.5 12.5 11.5
