The speed of a boat is 5km/h in still water. It crosses a river of width 1km along the shortest possible path in 20 minutes. The velocity of the river water is

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The speed of a boat is 5km/h in still water. It crosses a river of width 1km along the shortest possible path in 20 minutes. The velocity of the river water is

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5 km/h

3 km /h

1 km/h

4 km/h

answer is C.

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Detailed Solution

Time to cross the river in shortest time is

$\begin{array}{l} t = \frac{w}{\sqrt{v_{B}^{2} - v_{R}^{2}}} \\ or \frac{20}{60} = \frac{1}{\sqrt{25 - v_{R}^{2}}} or v_{R} = 4 Km / hr \end{array}$

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