Question

A visitor is staying in a tent that is 10 miles west of the closest point on a shoreline to a coral reef. The coral reef is 5 miles due south of the shoreline. The visitor plans to travel from the tent to the coral reef by running and swimming. If the visitor runs at a rate of 8 mph and swims at a rate of 1 mph, how far should the visitor run to minimize the time it takes to reach the coral reef?

Answer 1

To minimize the time it takes to reach the coral reef, the visitor should run 0 miles.

Step-by-step explanation:

To minimize the time it takes to reach the coral reef, the visitor should run to a point on the shoreline that is directly south of the coral reef. This will allow the visitor to swim directly to the reef without any additional distance to cover.

First, let's find the distance from the tent to the shoreline. The tent is 10 miles west of the closest point on the shoreline. Since the visitor plans to swim south, this distance is irrelevant for minimizing the time.

Next, we need to find the distance from the shoreline to the reef. The reef is 5 miles due south of the shoreline.

Therefore, the visitor should run 0 miles to minimize the time it takes to reach the coral reef.