Question

A boat which has a speed of 5 km// hr in steel 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:

13

Explanation:

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Answer 2

⠀⠀⠀⠀⠀⠀SOLUTION

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GIVEN⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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

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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

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

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✨Velocity of the river = 3km/hr