Related Rates Problem

Question

A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 7 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

Answer 1

You need to define your coordinates. Man walks at dy/dt = 2 ft/s (N) starting at (0,0) and t = 0 and the woman is walking walking at dy/dt = - 7ft/s (South) starting at (500,0) and t = 5 min

The equations for these two in terms of t : Man y_M = 2(60t) (t in minutes) x_M=0

Woman y_W = -7*(60)(t-5) x_W=500 ft

You are asked about the rate of z, the distance between them, so we need the expression for z:

z = sqrt((y_M-y_W)² + (x_M-x_W)²) = ((120t+420(t-5))²+(500)²)^1/2

You can differentiate with respect to t

dz/dt = (1/2)((120t+420(t-5))²+500²)^-1/2 2(120t+420(t-5)) (120+420)

Now just plug in t = 15 minutes after checking my math.