A lifeguard can sprint on sand and swim in water

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

Problem

A lifeguard can sprint

8\text{ m/s}

on sand and swim

2\text{ m/s}

in water. She starts at point

S

on the beach. A swimmer in distress is located at point

D

, which is

50\text{ m}

down the shore and

30\text{ m}

offshore. The lifeguard runs

x

meters along the beach from

S

before entering the water and swimming straight to

D

. Find the value of

x

(to the nearest tenth of a meter) that minimizes the rescue time.