A water well is 120 ft deep. A 120 ft cable weighing 30 lbs hangs down from the top of the well. Attached to the end of the cable is a 6 lb bucket. At the bottom of the well, the bucket initially contains 25 lbs of water. As the bucket rises at a constant rate, the water leaks out of the bucket at a constant rate such that the bucket contains 10 lbs of water the instant it reaches the top of the well. Find the work required to haul the leaky bucket up from the bottom to the top of the well.

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