math question based on related rates

Question

A ladder 26 ft long rests on the (horizontal) ground and leans against a (vertical) wall. The base of the ladder is pulled away from the wall at a rate of 4 ft/sec. How fast is the top of the ladder sliding down the wall when the base is 10 ft from the wall?

Answer 1

5/3 = 1 2/3 = about 1.67 feet per second is the speed of the top of the ladder sliding down the wall

call the position of the top of the ladder' distance to the ground "h"

call the distance from the bottom of the ladder to the wall "b"

h^2 + b^2 = 26^2 take derivatives

2hh' + 2bb' = 0

hh' + bb' =0

solve for h'

h' =-bb'/h = 10(4)/24 = 40/24 = 5/3 ft/sec = speed of top of the ladder

h^2 = 26^2 - b^2 = 676 -100 = 576

h = sqr576 = 24