A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 3.25 ft/s. How fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 4 ft above the ground? Solution: Let x be the distance from the bottom of the ladder to the wall, and let y be the distance from the top of the ladder to the ground. Draw a labeled sketch! The related variables equation is Related Variables Equation: = 324 Implicitly differentiate both sides of the related variables equation with respect to t, using x' for 4 and y' for dy The related rates equation is dt Related Rates Equation: Therefore, a formula for the rate at which the bottom of the ladder is sliding away from the wall is dr x' = dt Finally, when the top of the ladder is 4 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is da ft/s dt