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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

10. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio fo the speed of the train to that of the car is :
 
  • A. 3:3 km
  • B. 3:5 km
  • C. 3:4 km
  • D. 2:3 km
Ans: C.
Sol.
Let the speed of the train b x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/5
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24
Soving (i) and (ii), we get x = 60 and y = 80. ∴ Ratio of speeds = 60 : 80 = 3:4.
 
11. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is :
 
  • A. 52 km
  • B. 62 km
  • C. 55 km
  • D. 50 km
Ans: D.
Sol.
Let the actual distance travelled be x km. Then,
x/10 = (x+20)/14
⇔ 14x = 10x + 200
⇔ 4x = 200
x = 50 km.
 
 
12. Three persons are walking from a place A to another place B. Their speeds are in the ratio of 4 : 3 : 5. The time ratio to reach B by these
persons will be :
 
  • A. 4 : 3 : 5
  • B. 15 : 20 : 12
  • C. 5 : 3 : 4
  • D. 20: 15 : 12
Ans: B.
Sol.
Ratio of speeds = 4 : 3 : 5
∴ Ratio of times taken = 1/4 : 1/3 : 1/5 = 15 : 20 : 12.