1. While covering a distance of 49 km, a man noticed that after walking for 2 hours 20 minutes, the distance covered by him was 3/4 of the remaining distance. What was his speed in meters per second?
Solution:
Let x be the speed.
Distance covered in 2 hours 20 minutes = x*2(20/60) = x* 2(1/3) = 7x/3 km.
Remaining distance = (49- 7x/3) km.
7x/3 = 3/4 (49- 7x/3)
By solving the above equation, we get
x = 9 km/hr = 9*(5/18) = 2(1/2) m/sec.
2. A man travelled from the village to the post-office at the rate of 20 kmph and walked back at the rate of 5 kmph. If the whole journey took 2 hours 30 minutes, find the distance of the post-office from the village.
Solution:
Average speed = (2*20*5)/(20+5) = 8.
The whole distance travelled = 8*2(1/2) = 8*5/2 = 20 km.
Distance between the post-office and the village = 20/2 = 10 km.
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