At 12 noon ship A is 60 miles west of point P steaming east at 15 knots and ship B is 36 miles south of P steaming north at 10 knots. If the ships continue their courses and speed. how is the distance between them changes at 2pm? At what time the ships are closest?

Question

At 12 noon ship A is 60 miles west of point P steaming east at 15 knots and ship B is 36 miles south of P steaming north at 10 knots. If the ships continue their courses and speed. how is the distance between them changes at 2pm? At what time the ships are closest? 
The answers are 17.94 mph and 3.53pm, but i don't know how to get that. I convey knots to mph and my answers is always around 20.61 mph. Please help.

Steve · Answer

Why are you looking for speeds? The question is about distance.

Let's assume that the miles are nautical miles, so no conversions are necessary.

At time t hours, the distance z is found using

z^2 = (60-15t)^2 + (36-10t)^2
= 325t^2 - 2520t + 4896

2z dz/dt = 650t - 2520
The ships are closest when
dz/dt = 0 at t=3.877 = 3:52 pm

at 2:00, (t=2), z = 30.26
So, 60.52 dz/dt = 1300-2520
dz/dt = -20.15
so the ships are approaching each other at 20.15 knots

Actually, I think that the actual conversion ratio of knots to mi/hr is irrelevant, since the same scale factor will be used throughout.