OK,skeeter, if you read this, I need your help one last time.

A 5 lb bucket that is leaking is lifted from the ground into the air by a worker pulling 20 ft of rope at a constant speed. The rope weighs 0.08 lb/ft.

The bucket starts with 2 gallons of liquid. Each gallon of liquid weighs 16 pounds. The liquid leaks at a constant rate. It finishes leaking (becomes empty) just as it reaches the top. Find the work done.

Tell me what parts I have correct and correct me where I need correcting.

The interval that is sliced is [0,20] because it is the distance the bucket travels?

Since the weight of the rope changes as it is pulled up, we would have

.08(20-yi)

How do I also factor in the liquid in the bucket?