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

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

$60$ ft per minute. Similar triangles give lamp height $h$ with $\tfrac{h}{10+15}=\tfrac{6}{15}$, so $h=10$. In general $\tfrac{s}{6}=\tfrac{x+s}{10}$, so $s=1.5x$ and $s'=1.5\cdot40=60$, independent of the distance.