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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

13. In covering a distance of 30 km, Amla takes 2 hours more than Peter. If Amla doubles his speed, then he would take 1 hour less than Peter. Amla’s speed is :

• A. 7 kmph
• B. 6.5 kmph
• C. 5.5 kmph
• D. 5 kmph
 Ans: D. Sol. Let Peter’s speed be x km/hr. Then, 30/x - 30/2x = 3 ⇔ 6x = 30 ⇔ x = 5 km/hr

14. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

• A. 10
• B. 15
• C. 20
• D. 30
 Ans: A. Sol. Due to stoppages, it covers 9 km less. Time taken to cover 9 km = [9/54 * 60] min = 10 min.

15. A train when moves at an average speed of 40 kmph, reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of journey.

• A. 70 km
• B. 80 km
• C. 40 km
• D. 20 km
 Ans: A. Sol. Difference between timings = 15 min = 1/4 hr. Let the length of journey be x km. Then, x/35 - x/40 = 1/4 ⇔ 8x - 7x = 70 ⇔ x = 70 km.