Question

At noon, ship A is 50 km west of ship B. Ship A is sailing south at 10 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.)

Answer 1

So  hmmm check the picture below

so, we're looking for dr/dt then at 4:00pm or 4 hours later

now, keep in mind that, the distance "x", is not changing, is constant whilst "y" and "r" are moving, that simply means when taking the derivative, that goes to 0

$\bf r^2=x^2+y^2\implies 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad \begin{cases} \cfrac{dy}{dt}=30\\ r=130\\ y=120 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{120\cdot 30}{130}$