A 20m ladder is leaning against a wall. Top of ladder is sliding down at 3m per second and the bottom is sliding away from the wall at 4m per second. How high is the top of the ladder and far is the bottom of the ladder from the wall.

Answer 1

h = height up wall

d = distance from wall

by Pythagoras... h² + d² = 20²

differentiating
... 2 h dh/dt + 2 d dd/dt = 0

substituting
... (2 * h * -3) + (2 * d * 4) = 0
... 8 d = 6 h ... d = ¾ h

h² + (¾ h)² = 400

solve for h

substitute back to find d

Answer 2

Thanks, Scott! I got the height as 16 and distance as 12m.