A bucket that weighs 5 pounds and a rope of negligible weight are used to draw water from a well that is 81 feet deep. The bucket is filled with 37 pounds of water and is pulled up at a rate of 2.3 feet per second, but water leaks out of a hole in the bucket at a rate of 0.4 pounds per second. Find the work done pulling the bucket to the top of the well.
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