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A Bucket Weighs 5lb5 \mathrm { lb } And a Rope of Negligible Weight Are Used to Draw

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A bucket weighs 5lb5 \mathrm { lb } and a rope of negligible weight are used to draw water from a well that is 40 ft\mathrm { ft } deep. The bucket starts with 50lb50 \mathrm { lb } of water and is pulled up at a rate of 10ft/s10 \mathrm { ft } / \mathrm { s } , but water leaks out of a hole in the bucket at a rate of 0.5lb/s0.5 \mathrm { lb } / \mathrm { s } . Find the work done in pulling the bucket to the top of the well.


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