Related rates practice question 11

One ship heads north and the other east, so the port and the two ships form a triangle. What kind of triangle is it, and which side is the distance you want?

Let $x$ be B’s distance east and $y$ be A’s distance north. The distance between them is $d = \sqrt{x^{2} + y^{2}}$, so $d^{2} = x^{2} + y^{2}$ at every instant.

Differentiate $d^{2} = x^{2} + y^{2}$, then substitute $x = 40$, $y = 30$, $x' = 15$, $y' = 20$, and $d = 50$.