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## TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULAE

1. Speed = [Distance/Time],Time=[Distance/Speed],Distance = (Speed*Time) x km/hr = [x*5/18] m/sec. 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. x m/sec = [x*18/5] km/hr. 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. 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 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

7. A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A?

• A. 62.6 km
• B. 26.7 km
• C. 22.8 km
• D. 19.5 km
 Ans: B. Sol. Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours. ∴ x/4 - x/10 = 4 or x = 26.7 km.

8. A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at:

• A. 5.30 a.m
• B. 6.42 a.m
• C. 7.55 a.m
• D. 7.42 a.m
 Ans: D. Sol. Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two Relative speed of A and B = (6-1) = 5 rounds per hour. Time taken to complete one round at this speed = 1/5 hr = 12 min.

9. Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?

• A. 12 hrs
• B. 14 hrs
• C. 15 hrs
• D. 17 hrs
 Ans: D. Sol. to be 0.5 km apart, they take 1 hour. To be 8.5 km apart, they take [1/0.5 * 8.5] hrs = 17 hrs.