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A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

1. 3
2. 4
3. √21
4. 1

Correct answer: 4

Solution

The shortest path occurs when the boat's velocity is directed perpendicular to the riverbank. The boat's speed in still water is 5 km/hr, and it takes 15 minutes (0.25 hours) to cross 1 km. Thus, the boat's effective speed perpendicular to the river is 1/0.25 = 4 km/hr. Using Pythagoras' theorem, the river's velocity is √(5² - 4²) = √9 = 3 km/hr.

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