An island is 2 miles due south of its closest point along a straight shoreline. A visitor is staying in a cabin that is 7 miles west of that point. The visitor is planning to go from the cabin to the island. Suppose the visitor runs at a rate of 5 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the island?

Question
Asked Mar 24, 2019
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An island is 2 miles due south of its closest point along a straight shoreline. A visitor is staying in a cabin that is 7 miles west of that point. The visitor is planning to go from the cabin to the island. Suppose the visitor runs at a rate of 5 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the island?

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Expert Answer

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Step 1

Model the given problem as below.

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Step 2

Find BC with respect to x.

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Step 3

Find the time taken for running and swimming...

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Tagged in

Math

Calculus

Derivative