Question

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?

Step 1

Observe the given information and draw a sketch for it as shown in below Figure.

Step 2

From the Figure, it is observed that a right triangle is formed.

*EG* is hypotenuse side which is unknown.

Obtain the *EG* by Pythagoras theorem.

Step 3

Consider *t*1 and *t2* as the time took along *EF* and *EF*.

Now obtain the time...

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