Posted by **Amy** on Wednesday, November 2, 2011 at 10:27pm.

A 20' ladder leans against a building. The bottom of the ladder is sliding away horizontally at a rate of 2 feet per second. How fast is the top of the ladder sliding down the building when it is 12' above the ground?

- Calculus -
**Steve**, Thursday, November 3, 2011 at 4:53pm
If you draw a diagram, let x be the distance of the base of the ladder from the wall, and h the height of the ladder against the wall:

x^2 + h^2 = 400

When h = 12,

x^2 = 400 - 144 = 256

x = 16

2x dx/dt + 2h dh/dt = 0

32 * 2 + 24 dh/dt = 0

dh/dt = -64/24 = -8/3

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