A 10-foot ladder leans against a wall. The bottom slides away from the wall at 3 ft/s. How fast is the top sliding down when the bottom is 6 feet from the wall?

Core Concept

When $x=6$, the height is $y=\sqrt{10^2-6^2}=8$. From $x^2+y^2=100$, $\dfrac{dy}{dt}=-\dfrac{x}{y}\dfrac{dx}{dt}=-\dfrac{6}{8}(3)=-\dfrac{9}{4}$ ft/s.