Question

Boats A and B leave the same place at the same time. Boat A heads due North at 12 km/hr. Boat B heads due East at 18 km/hr. After 2.5 hours, how fast is the distance between the boats increasing?

You are looking at a right-angled triangle, let S be the distance between them

Then S^2 = (12t)^2+(18t)^2=468t^2

then 2S dS/dt = 936t when t-2.5, S = 2925 km

So dS/dt = 936(2.5)/(2x2925) = 0.4 km/h

Actually i figured it. But the correct answer is 21.63 km/hr. Thanks anyways.

of course Mischa, you are right, it looks like I did not take the square root of my S.
Good for you for being alert.