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TIME AND DISTANCE PROBLEMS

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TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULAE

1. Speed = [Distance/Time],
Time=[Distance/Speed],
Distance = (Speed*Time)
2. x km/hr = [x*5/18] m/sec.
3. If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is 1/a : 1/b or b:a.
4. x m/sec = [x*18/5] km/hr.
5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. then, the average speed during the whole journey is [2xy/x+y] km/hr.

TIME AND DISTANCE -> EXAMPLES

1. How many minutes does John take to cover a distance of 400 m, if he runs at a speed of 20 km/hr?
  Sol. John’s speed = 20 km/hr
= [20*5/18] m/sec
= 50/9 m/sec.
2. While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minute, the distance covered by him was 5/7 of the remaining distance. What was his speed in metres per second?
  Sol. Let the speed be x km/hr.
Then, distance covered in 1 hr: 40 min. i.e., 1 2/3 hrs = 5x/3 km.
Remaining distance = [24-5x/3] km.
5x/3 = 5/7[24-5x/3] 5x/3 = 5/7[72-5x/3] 7x = 72-5x
12x = 72 x = 6
Hence, speed = 6 km/hr = [6*5/18] m/sec = 5/3m/sec = 1 2/3 m/sec
3. If a man walks at athe rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
  Sol. Let the required distance be x km.
Difference in the times taken at two speeds = 12 min = 1/5 hr.
x/5 - x/6 = 1/5 6x - 5x = 6 x = 6.
Hence, the required distance is 6 km.

TIME AND DISTANCE -> EXERCISE

31. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations.
 
  • A. 8 : 10
  • B. 9 : 20
  • C. 11 : 9
  • D. 11 : 20
Ans: C.
Sol.
In the same time, they cover 110 km and 90 km respectively.
∴ Ratio of speeds = 110 : 90 = 11 : 9.
 
32. An athlete runs 200 metres race in 24 seconds. His speed is
 
  • A. 20 km / hr
  • B. 24 km /hr
  • C. 28.5 km / hr
  • D. 30 km / hr
Ans: D.
Sol.
Speed = 200 / 24 m/sec = 25 / 3 m/sec
= (25/3 x 18 / 5) km / hr = 30 km / hr.
 
 
33. Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
 
  • A. 120 km
  • B. 360 km
  • C. 480 km
  • D. 500 km
Ans: C.
Sol.
Suppose they meet x hours after 14.30 hrs.
Then, 60x = 80 (x - 2) or x = 8.
∴ Required distance = (60x8)km = 480 km.