Question

Francis starts walking north at 4 ft/s from an intersection I. At the same time Aram starts walking south at a
rate of 5 ft/s from a intersection 1500 ft due east of I. At what rate are they moving apart 15 minutes later?
(Rounding to 1 decimal place is fine.)

Answer 1

the separation distance d at time t is given by

d^2 = (4t+5t)^2 + 1500^2
d^2 = 81t^2 + 2250000

2d dd/dt = 162t

d^2 at t=15min = 900 sec = 81*900^2 + 1500^2
= 100^2 * (81*81 + 15*15)
d = 100 * sqrt(6786)
d = 8237.719

dd/dt = 162(900)/16475.438 = 8.85

That looks reasonable. It's less than 9, but pretty close, since at 8237 ft apart, the initial 1500-ft separation is relatively small.