# Math Help - Rate of Change: Ladder Problem

1. ## Rate of Change: Ladder Problem

I hope I get a response today...haha. Anyways, if anyone could help me figure this problem out. It'll be greattt...

A math teacher is on top of a 20 foot ladder leaning against a wall when the bottom starts to slip away from the wall. The bottom of the ladder is moving away from the wall at 3 feet per second. How fast is the math teacher approaching the ground when they are 12 feet from the ground?

2. These ladder slipping problems are among the most over-used with regards to related rates.

We know y=12, dx/dt=3, and can easily find x.

If the top of the ladder is 12 feet off the ground, then the base is $x=\sqrt{20^{2}-12^{2}}=16$ feet from the wall.

$x^{2}+y^{2}=20$

differentiate wrt time:

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$

Now, enter in your knowns and solve for dy/dt.