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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

25. A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is :

• A. 1
• B. 2
• C. 3
• D. 4
 Ans: C. Sol. Let the total distance be 3x km. Then, x/3 + x/4 + x/5 = 47/60 ⇔ 47x/60 = 47/60 ⇔ x = 1. ∴ total distance = (3*1) km = 3km.

26. A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5 km on foot. His total journey is :

• A. 125 km
• B. 130 km
• C. 135 km
• D. 140 km
 Ans: B. Sol. Let the total journey be x km. Then 3x/5 + 7x/20 + 6.5 = x ⇔ 12x + 7x + 20 * 6.5 = 20x ⇔ x = 130 km.

27. A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be :

• A. 7 km/hr
• B. 8 km/hr
• C. 11 km/hr
• D. 12 km/hr
 Ans: D. Sol. Remaing distance = 3 km and Remaining time = [1/3 * 45] min = 15 min = 1/4 hour. ∴ Required speed = (3*4) km/hr = 12 km/hr.