Question

Bob has a tree house at a height of 20 ft. When he's feeling adventurous he uses a rope to climb the tree house instead of the ladder. If the weight of the rope is 32 lb, then how much work must Bob do to pull the rope up once he has entered the house?

Answer 1

I believe work = force*distance
W = 32*20

Answer 2

The lb/ft = 32/20 = 8/5. From this we can build the integral:
\[\int\limits_{0}^{20}(\frac{8}{5}x)dx=\frac{8}{5}\int\limits_{0}^{20}xdx=\frac{8}{5}[\frac{x^2}{2}]_0^{20}=\frac{8}{5}\frac{400}{2}=\frac{1600}{5}=320\]