Question

A bucket weighing 4 lbs and a rope weighing 0.07 lb/ft are used to draw water from a well that is
65 ft deep. The bucket starts with 40lbs of water and is pulled up at a rate of 5 ft/s, but water
leaks out of a hole in the bucket at a rate of 0.5 lb/s. Find the work done in pulling the bucket to
the top of the well