A25-ft ladder rests against a vertical wall. if the bottom of the ladder slides away from the wall at a rate of 0.18 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 20 ft from the wall? answer with 2 decimal places.

Let be the distance between the base of the ladder and the bottom of the wall, and the distance between the top of the ladder and the bottom of the wall, so that

Differentiate both sides with respect to time :

When , the top of the ladder is

above the ground. Then, given that the bottom of the ladder slides away from the wall at a rate of , we have

That is, the top of the ladder is sliding downward at a rate of 0.24 ft/s.

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