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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

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.