Chapter 6.6, Problem 22ES

A $3\text{ lb}$ bucket containing $20\text{ lb}$ of water is hanging at the end of a $20\text{ ft}$ rope that weighs $4\text{ oz/ft}$ . The other end of the rope is attached to a pulley. How much work is required to wind the length of rope onto the pulley, assuming that the rope is wound onto the pulley at a rate of $2\text{ ft/s}$ and that as the bucket is being lifted, water leaks from the bucket at a rate of $0.5\text{ lb/s}$ ?