A tank, with a rectangular base and having vertical sides of height 4 m, is initially full of water. The water leaks out of a small hole in the horizontal base of the tank at a rate which, at any instant, is proportional to the square root of the depth of the water at that instant.

Question

A tank, with a rectangular base and having vertical sides of height 4 m, is initially full of water. The water leaks out of a small hole in the horizontal base of the tank at a rate which, at any instant, is proportional to the square root of the depth of the water at that instant.
If x is the depth of water at time t after the leak started, write down a differential equation connecting x and t. If the tank is exactly half empty after one hour, find the further time that elapses before the tank becomes completely empty.