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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

34. A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40 km / hr. In the return trip, he covers the same distance at an average speed of 20 km / hr. The average speed of the car over the entire distance of 400 km / hr.
 
  • A. 22 km/hr
  • B. 28.56 km/hr
  • C. 26.67 km/hr
  • D. 30 km/hr
Ans: C.
Sol.
Average speed = (2×40×20 / 40 + 60) km/hr
= (80/3)km/hr
= 26.67 km/hr.
 
35. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
 
  • A. 5 a.m.
  • B. 10 a.m.
  • C. 10.30 a.m.
  • D. 11 a.m.
Ans: D.
Sol.
Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs)+[Distance moved by second in (x-1)hrs] = 330.
∴ 60x + 75(x-1) = 330 ⇒ x = 3.
So, they meet at (8 + 3), i.e. 11 a.m.
 
 
36. An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
 
  • A. 5 hrs 20 min
  • B. 6 hrs 21 min
  • C. 6 hrs 24 min
  • D. 6 hrs 30 min
Ans: B.
Sol.
Time taken to cover 600 km = (600 / 100) hrs = 6 hrs.
Number of stoppages = 600 / 75 - 1 = 8 -1 = 7.
Total time of stoppages = (3x7) min = 21 min.
Hence, total time taken = 6 hrs 21 min.