Related Rates hw problem

Question

A man starts walking north at 4ft/s from a point P. Five minutes later, a woman starts walking south at 5ft/s from a point 500ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?\

________ ft/s

Answer 1

D istance d(t) t minutes after woman start d(t) = [500² + (4(t + 15) + 5t)²]^1/2 = (250000 + (9t + 60)²]^1/2.

d'(t) = 9(9t + 60)/[250000 + (9t + 60)²]^1/2

d'(15) = 9(9··15 + 60)/[250000 + (9·15 + 60)²]^{1 /2} = 3.27/ft/min