A ship, proceeding southward on a straight course at the rate of 12 miles/hr is, at noon,

Question

40 miles due north of a second ship, which is sailing west at 15 miles/hr.
a) How fast are the ships approaching each other 1 hour later?

Answer 1

Let t hours be any time after noon
Make a sketch of that position.
Let the distance between them be D miles
I have a right-angled triangle and
D^2 = (15t)^2 + (40-12t)^2
2D dD/dt = 2(15t)(15) + 2(40-12t)(-12)

when t = 1, D^2 = 15^2 + 28^2
D = √1009

then when t = 1
dD/dt = .....