Integrating to Find Work

Isabella built a treehouse 20 m off the ground. She has a rope going from the top to the bottom which weighs 0.6 kg/m. Attached to the rope is an old bucket that weighs 10 kg.

Her friend below fills the bucket up with 60 kg of Kool-Aid. Isabella pulls the rope and bucket up with a constant speed. Sadly, the bucket has a hole in it and leaks at a constant rate. At the exact moment Isabella pulls the bucket up to the top, the bucket has drained completely.