How fast is the distance between the ships changing at 4:00 PM?

Question

At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer 1

A^2 + B^2 = D^2

2 A dA/dt + 2 B dB/dt = 2 D dD/dt

A dA/dt + B dB/ dt = D dD/dt

dA/dt = -40

dB/dt = 15

At 4 hours, A=170 - 4*40 = 10 and B = 4*15=60 ---> D = sqrt( 100 + 3600) = sqrt(3700) =

10*sqrt(37)

10 * -40 + 60 * 15 = 10 * sqrt(37) * dD/dt

-400 + 900 = 10 * sqrt(37) dD/dt

500 = 10 * sqrt(37) dD/dt

50 * sqrt(37)/37 = dD/dt