A man rowing at the rate of $5$ km an hour in still water takes thrice as much time in going $40$ km up the river as in going $40$ km down.Find the rate at which the river flows.

12

km/hr

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9.5

km/hr

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2.5

km/hr

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15

km/hr

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Solution

The correct option is C $2.5$ km/hr
Lets assume that river flows at $V$ km/hr.
Upstream velocity $= (5 - V)$ km/hr
Downstream velocity $= (5 + V)$ km/hr
As he travels equal distance in both directions.
$T_{u p} (5 - V)$ $=$ $T_{d o w n} (5 + V)$ , where $T_{u p}$ and $T_{d o w n}$ are time taken for upstream and downstream travelling respectively.
It is given that $T_{u p} = 3 T_{d o w n}$
Therefore, $3 (5 - V) = 5 + V$
$\Rightarrow V = 2.5$ km/hr

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A man rowing at the rate of 5 km an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down.Find the rate at which the river flows.

A man rowing at the rate of $5$ km an hour in still water takes thrice as much time in going $40$ km up the river as in going $40$ km down.Find the rate at which the river flows.