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