I just need an integral to express this situation: A bucket that weighs 3 lb and a rope of negligible weight are used to pull water out of a well that is 60 ft deep. Suppose the bucket starts with 37lb of water and is pulled by a rope at 2 ft/sec while water leaks from the bucket at a rate of 1/4 lb/sec. How does it take for the bucket to reach the top of the well?

Question

anonymous · Answer

I just need an expression...

anonymous · Answer

There is nothing in your problem that states that the rate bucket is travelling is varying.  So it seems to me that there is nothing to integrate.

anonymous · Answer

I would make sure you have the problem down correctly.

anonymous · Answer

What IS changing is the weight of the water in the bucket and, in turn, the work being done.

anonymous · Answer

I see that, but aren't asking how long it takes for the bucket to reach the top of well? If you are pulling the rope at a constant rate, then it's just a simple division problem.

anonymous · Answer

That may be true, there are separate portions to the problem...

anonymous · Answer

Now if you where asking what the weight of the bucket and any water in the bucket when it gets to the top, now you have something that is changing with time.