1. The problem statement, all variables and given/known data From Stewart Calculus Concepts and Contexts 4th edition pg.473 section 6.6 #15... :A leaky 10-kg bucket is lifted from the ground to a height of 12 meters at a constant speed with a rope that weighs 0.8kg/m. Initially the bucket contains 36kg of water but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12 meter level. How much work is done 2. Relevant equations 3. The attempt at a solution I am able to do these kind of problems, but the only thing different about this one is the weight is constantly changing. The total weight of the water/bucket/rope initially is 55.6 kg, and at the end its just the 10 kg bucket left. I dont know how to approach the change in weight of the water leaking out of the bucket. So far I think you integrate from 0-12 meters, and the distance an arbitrary part of the rope has to travel is 12-x. Any hints?