a ladder is 20 feet long and its top is slidding at a constant rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground when the bottom is 16 feet from the wall?

Answer 1

Let the ladder be x ft from the wall, and y ft up along the wall
x^2 + y^2 = 20^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
when x=16 , y^2 = 400-256 ---> y = 12
and dy/dt = -2 ft/sec

16(dx/dt) + 12(-2) = 0
dx/dt = -24/16 = -3/2

the ladder is moving away from the wall at 1.5 ft/s

Answer 2

last two lines should have been

16(dx/dt) + 12(-2) = 0
dx/dt = 24/16 = 3/2