A leaky bucket that weighs 4 lb and a rope of neglible weight are used to draw water from a well that is 406 ft deep.

A leaky bucket that weighs 4 lb and a rope of neglible weight are used to draw water from a well that is 406 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 5 ft/sec, but water leaks out of the bucket at a rate of 0.5 lb/sec. Find the work done in pulling the bucket to the top of the well