Growth rate of a walker's shadow from a lamp post

A $6$-ft-tall person walks directly away from a street lamp at $40$ ft per minute. When they are $10$ ft from the post, their shadow measures $15$ ft. How fast is the shadow lengthening, in ft per minute, when they are $40$ ft from the post?

$60$ ft per minute. Similar triangles give the lamp height: $h/25=6/15$, so $h=10$. Then $10/(x+s)=6/s$ gives $s=\tfrac32x$, so the shadow always grows at $\tfrac32\cdot40=60$ ft/min, at any distance.