A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is

A person rows a boat in still water at 5 km/hr. When rowing in a river, the current helps when going downstream but works against when going upstream. Going upstream takes 4 times as long as going downstream for the same distance.

Let the speed of stream $= s$ km/hr

Downstream speed $= 5 + s$ km/hr (current helps push the boat)

Upstream speed $= 5 - s$ km/hr (current pushes against the boat)

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Let distance $= d$ km (same for both directions)

Time $= \dfrac{\text{Distance}}{\text{Speed}}$

Time taken downstream $= \dfrac{d}{5 + s}$

Time taken upstream $= \dfrac{d}{5 - s}$

Given that upstream time $= 4 \times$ downstream time:

$\dfrac{d}{5 - s} = 4 \times \dfrac{d}{5 + s}$

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Distance $d$ cancels from both sides:

$\dfrac{1}{5 - s} = \dfrac{4}{5 + s}$

$5 + s = 4(5 - s)$

$5 + s = 20 - 4s$

$s + 4s = 20 - 5$

$5s = 15$

$s = 3$ km/hr

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Therefore, the speed of the stream is 3 km/hr.