Question

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?

Answer 1

Answer:

Speed of the boat in still water = 5 km/hr

Width of the river (AB) = 1 km

Time taken by the boat to cross the river = 15 minutes = 1/4 hr

Let the velocity of the river be x km/hr.

Distance covered by the boat in 15 minutes = 1.25 km

Because of the flow of the river, the boat will move in the direction of AC, which is the shortest possible path for the boat

AC = 1.25 km

AB = 1 km

BC is the other bank of the river so the width AB of the river will be perpendicular to BC.

∠B = 90°

Apply Pythagoras theorem in ΔABC  

(AB)2 + (BC)2 = (AC)2

BC = 0.75 km

So, the distance covered by the river water in 15 minutes is 0.75 km.

Velocity of the river = 0.75/(1/4) = 3 km/hr

Answer 2

Explanation:

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