MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A lifeguard stands at point A on a straight beach. A swimmer in distress is at point B, which is 60 m directly offshore and 90 m down the shoreline from A. The lifeguard can run at 8 m/s on sand and swim at 2 m/s in water. If the lifeguard runs x meters along the shoreline before entering the water and then swims straight to B, which value of x (to the nearest meter) yields the least travel time?
(a) 72 m
(b) 75 m
(c) 82 m
(d) 45 m