Speed of a ladder top as its oily foot slides out

A ladder $50$ ft long leans against a vertical wall. Its foot rests on oil and slides directly away from the wall at a steady $4$ ft per minute, so the top slides down the wall. At the moment the foot is $30$ ft from the wall, how fast (in ft per minute) is the top moving down?

$3$ ft per minute. With foot distance $x$ and top height $y$, $x^2+y^2=2500$. At $x=30$, $y=40$. Differentiating, $xx'+yy'=0$, so $y'=-\tfrac{30\cdot4}{40}=-3$: the top descends at $3$ ft per minute.