A lifeguard runs at on the beach and swims at in the water

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A lifeguard runs at

5\text{ m/s}

on the beach and swims at

2\text{ m/s}

in the water. The lifeguard is

40\text{ m}

downshore from a point on the beach directly opposite a swimmer who is

30\text{ m}

offshore. The lifeguard runs straight along the beach to a point

x

metres from the point opposite the swimmer before entering the water and swimming straight to the swimmer. Determine the value of

x

that minimizes the total rescue time.