A man rows to a place 48 km distance and back in 14 hours. He find that he can row 4km with the stream in the same time as 3 km against the stream. Find the rate of stream.

Solution(By Examveda Team)

Let the speed of boat in still water be v km/hr and speed of stream be u km/hr.
From the first information given,
Total time = 14 hr.
Total time = Time taken along upstream + Time taken along downstream.
∴ (48 / (v+u)) + (48 / (v-u)) = 14
∴ 2 * v / (v² - u²) = 7 / 24 -------(1)
From the second information given,
∴ 4 / (v+u) = 3 / (v-u)
∴ v = 7 * u -------(2)
Putting equation (2) in equation (1),
∴ 2 * 7 * u / (49 * u²-u²) = 7 / 24
Solving it we get,
u = 1 and v = 7.
So speed of boat in still water is 7 km/hr and speed of stream is 1 km/hr.