Question

A man starts walking north at 4 ft/sec from point P. Five minutes later a woman starts walking south at 5 ft/sec from a point 500 ft due east of P. At what rate ae the people moving apart 15 minutes after the woman starts walking? Draw a diagram.

1) What rate is given? State answer in terms of variables from diagram.
2) What rate are you asked to find? State answer in terms of variables from diagram.
3) Find the required rate

Answer 1

at time t>=300 (5 min = 300 sec) the man has gone 4t ft north, and the woman has gone 5(t-300) ft south.

The distance d between them is thus

d^2 = 500^2 + (4t + 5(t-300))^2
= 81t^2 - 27000t + 2,500,000
at t=15 min = 900 seconds,
d = 6619 ft

2d dd/dt = 162t - 27000
so, at t=900
2(6619) dd/dt = 162(900)-27000
dd/dt = 8.97 ft/s

This makes sense, since the farther apart they are, the less the 500 ft between their paths matters, and their relative speed will approach 5+4=9 ft/s.