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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

34. A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40 km / hr. In the return trip, he covers the same distance at an average speed of 20 km / hr. The average speed of the car over the entire distance of 400 km / hr.

• A. 22 km/hr
• B. 28.56 km/hr
• C. 26.67 km/hr
• D. 30 km/hr
 Ans: C. Sol. Average speed = (2×40×20 / 40 + 60) km/hr = (80/3)km/hr = 26.67 km/hr.

35. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?

• A. 5 a.m.
• B. 10 a.m.
• C. 10.30 a.m.
• D. 11 a.m.
 Ans: D. Sol. Suppose they meet x hrs after 8 a.m. Then, (Distance moved by first in x hrs)+[Distance moved by second in (x-1)hrs] = 330. ∴ 60x + 75(x-1) = 330 ⇒ x = 3. So, they meet at (8 + 3), i.e. 11 a.m.

36. An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?

• A. 5 hrs 20 min
• B. 6 hrs 21 min
• C. 6 hrs 24 min
• D. 6 hrs 30 min
 Ans: B. Sol. Time taken to cover 600 km = (600 / 100) hrs = 6 hrs. Number of stoppages = 600 / 75 - 1 = 8 -1 = 7. Total time of stoppages = (3x7) min = 21 min. Hence, total time taken = 6 hrs 21 min.