$\"\"$

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The man can row at $\"\"$ miles per hour and walk at $\"\"$ miles per hour.

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The angles are $\"\"$ and $\"\"$ .

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Draw a diagram.

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$\"\"$

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Observe the diagram:

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$\"\"$ and $\"\"$ .

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Here $\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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$\"\"$

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Time $\"\"$ .

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Time taken by the man to row in water is $\"\"$ .

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Time taken by the man to walk is $\"\"$ .

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Here the time is considered for the man can row in water and walking time.

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$\"\"$

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Find the minimum time taken, evaluate $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Equate $\"\"$ to zero.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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$\"\"$ .

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Thus, least time taken by man reaches to $\"\"$ when $\"\"$ .

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$\"\"$

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Least time taken by man reaches to $\"\"$ when $\"\"$ .