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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

22. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is :
 
  • A. 45.30 km/hr
  • B. 55.15 km/hr
  • C. 70.15 km/hr
  • D. 71.11 km/hr
Ans: D.
Sol.
Total time taken = [160/64 + 160/8] hrs = 9/2 hrs.
∴ Average speed = [320*2/9] km/hr = 71.11 km/hr.
 
23. A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. the distance between his house and school is :
 
  • A. 4.5 km
  • B. 5.5 km
  • C. 6 km
  • D. 7 km
Ans: C.
Sol.
Average speed = [2*3*2 / 3+2] km/hr = 12/5 km/hr.
Distance travelled = [12/5 * 5] km = 12 km.
∴ Distance between house and school = [12/2] km = 6 km.
 
 
24. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. The distance travelled on foot is :
 
  • A. 1 hr 16 min
  • B. 1 hr 17 min
  • C. 1 hr 18 min
  • D. 1 hr 19 min
Ans: A.
Sol.
Let the distance travelled on foot be x km.
then, distance travelled on bicycle = (61 - x) km.
So, x/4 + (61-x)/9 = 9
⇔ 9x + 4 (61 - x) = 9 * 36
⇔ 5x = 80
x = 16 km.