# A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. The island is 7 miles due south of the shoreline. The visitor plans to travel from the cottage to the island by running and swimming. If 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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A visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. The island is 7 miles due south of the shoreline. The visitor plans to travel from the cottage to the island by running and swimming. If 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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Step 1

The distance of the visitor’s cottage is 10 miles east of the closest point on a shoreline to an island. The distance between the island and the shoreline is 7 miles south of the shoreline. The visitor runs at a speed of 5 mph and swims at a speed of 3 mph.

If the visitor runs 10 miles at 5 mph, the time taken is

Step 2

If the visitor swims 7 miles at 3 mph, the time taken is

Step 3

Maximum time would be 4 h 20 m, unfortunately, the minimum time is required.

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