Weight of the bucket is  lb/ft.

Weight of the water in the bucket is  lb.

Total weight of bucket with water is  lb.

Depth of the well is  ft.

Bucket with water is pulled up at  ft/sec.

Leakage rate of water at the bottom of a hole in bucket is  lb/sec.

At any time , consider distance of bucket from bottom of the well as  ft.

.

Substitute ,  and  in above expression.

Weight of remaining water in the bucket is  lb.

Total weight of the bucket with water at any time  is .

Find the work done required to pull the bucket to the top of the well.

Work done as a Riemann sum is  .

 lb-ft.

Work done required to pull the bucket to the top of the well  lb-ft.