Question

A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an island. The island is 3 kilometers due south of the shoreline. The visitor plans to travel from the tent to the island by running and swimming. If the visitor runs at a rate of 6 km/h and swims at a rate of 5 km/h, how far should the visitor run to minimize the time it takes to reach the island?

Answer 1

A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an island, the time it takes to reach the island, the visitor should run approximately 7.62 km.

Step-by-step explanation:

To minimize the time it takes for the visitor to reach the island, they should run in a straight line towards the shoreline.

This is because the visitor will cover the ground distance much faster by running compared to swimming.

The distance the visitor needs to run can be found using the Pythagorean theorem.

The distance from the tent to the shoreline is 7 km, and the distance from the shoreline to the island is 3 km.

So, the visitor needs to run a distance equal to the hypotenuse of a right triangle with sides 7 km and 3 km.

Using the Pythagorean theorem, the distance the visitor needs to run is √(7² + 3²) = √(49 + 9) = √58 km, which is approximately 7.62 km.

Therefore, the visitor should run approximately 7.62 km to minimize the time it takes to reach the island.