$\"\"$

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Two people starts from the same point at $\"\"$ .

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One walks toward east with a speed of $\"\"$ mi/h.

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Other walks towards northeast with a speed of $\"\"$ mi/h.

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Therefore, $\"\"$ and $\"\"$ .

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$\"\"$

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Assume after some time $\"\"$ , first person reaches the point $\"\"$ and other one reach the point $\"\"$ .

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Let the sides of the triangle be considered $\"\"$ , $\"\"$ and $\"\"$ .

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One person moves east and other one moves northeast means angle between them is $\"\"$ .

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$\"\"$

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Apply cosine rule to the $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in above expression.

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$\"\"$

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

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$\"\"$

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Find the rate at which the change in the distance between them after $\"\"$ minutes.

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Distance travelled by the first person in $\"\"$ minutes is $\"\"$ mi.

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Distance travelled by the second person in $\"\"$ minutes is $\"\"$ mi.

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Find distance between the two persons after $\"\"$ minutes:

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Substitute corresponding values in above expression.

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$\"\"$

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Rate at which the change in the distance between them after $\"\"$ minutes is $\"\"$ .

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$\"\"$

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Rate at which the change in the distance between them after $\"\"$ minutes is $\"\"$ .