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
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.
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?