Related Rates Practice Problems

A 20 foot ladder is leaning against a wall and the base of the ladder is sliding away at 6 feet a second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet from the wall?

Let $y = \sin{(x)}$

Find $\frac{dy}{dt}$ when $x = \frac{\pi}{4}$ given $\frac{dx}{dt} = 2 \frac{cm}{sec}$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

Find the rate of change of the height of the water level if the hose is pouring $2 \frac{{ft}^3}{m}$