# 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 6mph 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 6mph 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

To calculate the distance of running by visitor that minimize the time for that it takes to reach the rock formation. The distance of rock formation is 3 miles due north. The visitor is staying on a tent which is 4 miles west. The visitor runs at the rate of 6 mph and swim at the rate of 3 mph. For the distance that minimize the time, first calculate the time function then derivative the function and equate to zero.

Step 2

Let p be the distance between point PQ, and q is the distance between point QS that is mentioned in the diagram and the provided diagram is shown below,

Step 3

Now, calculate the distance of QS, using Pythagoras theor...

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### Calculus 