Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west at 42 mi/h. At what rate is the distance between the cars increasing three hours later?

Answer 1

S^2 + W^2 = D^2

where S is the southbound car

W is the westbound car

D is the distance

2 * S dS/dt + 2 W dW/dt = 2 D dD/dt

S dS/dt + W dW/dt = D dD/dt

in 3 hours, S=3*56 = 168 and W = 3*42 = 126

and D = sqrt( 168^2 + 126^2) = 210

168 * 56 + 126 * 42 = 210 * dD/dt

(168 * 56 + 126 * 42) / 210 = dD/dt

dD/dt = 70