The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.9 m/s. How long is the ladder?

Let the length of the ladder be L we have comparing lengths after 1s and applying Pythagoras theorem.

(3 + 0.9*) ^2 + {√ (L^2-9) - 0.675*} ^2 = L^2 or

9 + 1.8 + 0.81 + (L^2-9) + 0.455625 - 1.35*√ (L^2-9) = L^2 or

√ (L^2-9) = 8.9375 or (L^2-9) = 79.87890625

or L = 9.43 m