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## Homework Statement

A bucket that weighs 80lbs when filled with water is lifted from the bottom of a well that is 75ft deep. The bucket has a hole in it and weighs only 40lb when it reaches the top of the well. The rope weighs 0.65 lb/ft. Find the work required to life the bucket from the bottom to top of the well.

## The Attempt at a Solution

Here is what I did:

Set the bottom a y=0 and top at y=75, and got the following:

[tex]W_{bucket}= 80 - \frac{40}{75}y[/tex]

[tex]W_{rope}= 48.75 - 0.65y[/tex]

So:

[tex]W_{total} = 128.75 - \frac{71}{60}y [/tex]

[tex]\int_{0}^{75} (128.75 - \frac{71}{60}y)75 dy[/tex]

Would that be the right integral set up?