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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?

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?
 
check_circleAnswer
Step 1

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

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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.

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Step 3

Consider t1 and t2 as the time took along EF and EF.

Now obtain the time...

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Math

Calculus

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