If x is the distance the base of the ladder is from the wall, and y is the distance to top of the ladder is up the wall, then the Pythagorean theorem tells you
... x² + y² = 10²
Differentiating with respect to time, we have
... 2x·dx/dt + 2y·dy/dt = 0
... dy/dt = (-x/y)·dx/dt
We are given x = 6 ft and dx/dt = 3 ft/s. Using the first equation, we can find y as
... y = √(10² -6²) = 8
Then
... dy/dt =(-6/8)·(3 ft/s)
... dy/dt = -2.25 ft/s
The top of the ladder is sliding down the wall at -2.25 ft/s.
