[2.5 km/hr] A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to r

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A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.

10 km/hr

2.5 km/hr

5 km/hr

7.5 km/hr

Explanation:

Given that, time taken to travel upstream = 2 × time taken to travel downstream

When distance is constant, speed is inversely proportional to the time

Hence, 2 × speed upstream = speed downstream

Let speed upstream $=x$

Then speed downstream $=2x$

we have, $\dfrac{1}{2}(x + 2x)$ = speed in still water

$\Rightarrow \dfrac{1}{2}(3x) = 7.5$

$\Rightarrow 3x = 15$

$\Rightarrow x = 5$

i.e., speed upstream = 5 km/hr

Rate of stream $=\dfrac{1}{2}(2x-x) = \dfrac{x}{2}= \dfrac{5}{2} = 2.5\text{ km/hr}$

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