# A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point. The visitor is planning to go from the tent to the rock formation. Suppose the visitor runs at a rate of 6 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the rock formation?

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A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point. The visitor is planning to go from the tent to the rock formation. Suppose the visitor runs at a rate of 6 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the rock formation?

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Step 1

Given A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point.

Step 2

Let,

x be the distance covered by running and y be the distance covered by swimming, so the figure will be

Step 3

By using the Pythagoras...

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