
related rates
Two boats are headed due north. Boat A is traveling at 25 ft/sec while Boat B is traveling at 15 ft/sec. Boat A is following a course which is 240 ft west of boat B. How fast is the distance between the boats changing when Boat A is 450 ft behind Boat B?

Problems like this call for ol' Pythagoras.
The boats are 240 feet apart. That is constant. Therefore, dx/dt=0
One is travelling at 25 ft/sec and the other at 15 ft/sec. 2515=10
dy/dt=10 ft/sec.
$\displaystyle D^{2}=x^{2}+y^{2}$
When x=240 and y=450, then D=510
Differentiate:
$\displaystyle D\frac{dy}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}$
$\displaystyle (510)\frac{dD}{dt}=240(0)+(450)(10)$
$\displaystyle \frac{dD}{dt}=\frac{150}{17} \;\ ft/sec$
Check my figures. I have done this in a hurry.