Question

$\Huge \fbox \red{☞Question}$
A boat which has a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minute. The velocity of the river in the shortest time. The velocity of river water in km/hr is [1988-1 mark]​

Answer 1

✮ Appropriate Question ✮

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• A boat which has a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minute. The velocity of the river in the shortest time. The velocity of river water in km/hr is [1988-1 mark]

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✮ Required Solution ✮

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Answer:

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

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• ➦ Width of the river (AB) = 1 km

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• ➦ 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.☯

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• ➦ Distance covered by the boat in 15 minutes = 1.25 km

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• ➦ 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

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• ➦ AC = 1.25 km

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• ➦ AB = 1 km

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

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• ➦ ∠B = 90°

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• ➦Apply Pythagoras theorem in ΔABC  ☑

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• ➦ (AB)² + (BC)² = (AC)²

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• ➦ 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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$\pink{\sf{\star\;➦\; Velocity \;of \;the\; river \;= 3 \;km/hr}}$

Answer 2

$\Huge \fbox \red{☞Question}$

A boat which has a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minute. The velocity of the river in the shortest time. The velocity of river water in km/hr is [1988-1 mark]

$\huge\red{\mid{\underline{\overline{\textbf{Solution\:࿐}}}\mid}}$

☆ 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.

$\sf\red{hope\:it\:helps\:you}$