Multiple choice

The width of river is 1 km. The velocity of boatis 5 km/hr. The boat covered the width of riverwith shortest will possible path in 15 min. Thenthe velocity of river stream is :

  1. 3 km/hr

  2. 4 km/hr
  3. $\sqrt { 29 } km/hr$
  4. $\sqrt { 41 } km/hr$
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A Correct answer
Explanation

The boat crosses the 1 km width in 15 minutes (0.25 hours). The resultant velocity is 1/0.25 = 4 km/hr. Since the boat moves with the shortest path, the velocity of the boat (5 km/hr) is the hypotenuse, and the river velocity (v) and resultant velocity (4 km/hr) are legs. 5^2 = 4^2 + v^2, so v = 3 km/hr.

AI explanation

The boat crosses the river along the shortest possible path in 15 minutes, which is 0.25 hours, giving an effective crossing speed perpendicular to the bank of 1 km divided by 0.25 hours, equaling 4 km/hr. Since the boat's speed in still water is 5 km/hr, we use the Pythagorean theorem to find the stream velocity: the river velocity squared equals the boat's still water speed squared minus the effective crossing speed squared. Substituting the values gives the stream velocity as the square root of (5 squared minus 4 squared), resulting in the square root of 9, which is 3 km/hr.

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