A heavy metal 2 pound bucket initially is filled with 10 pounds of paint. Immediately after it is filled, it is pulled up at a steady rate to the top of a building 30 feet high. While being pulled, the paint leaks out through a hole in the pail at a steady rate so that by the time it reaches the top, 1/5 of the paint has leaked out.
Let w(h) be the weight of the bucket at height h. First find w(h).
For this first part I got:
$$w(h) = 2+(10-{h\over15})$$
The second part asks:
Use the answer above to find the work. How many foot-pounds of work W were done pulling the bucket to the top of the building?
How do I find the work done?