Mathematics

Problem

A kayaker can run along a straight shoreline at

5\text{ m/s}

and paddle in still water at

3\text{ m/s}

. Point

A

is on the shore, and point

B

800\text{ m}

farther down the shore and

300\text{ m}

offshore. The kayaker runs

x

meters from

A

along the shore before entering the water and paddling straight to

B

. Determine the value of

x

(to the nearest meter) that minimizes the total travel time.