1. The problem statement, all variables and given/known data A leaky 6lb bucket is lifted from the ground to a height of 30ft at a constant speed with a rope that weighs .5lb/ft. Initially, the bucket contains 60lbs of water, but the water leaks out at a constant rate and finishes draining just as the bucket reaches the 30ft level. How much total work is done lifting the bucket? 2. Relevant equations Function I found for the weight of the rope: (15-.5x) Function I found for the weight of the bucket: (60-2x) so adding all together I got = 6 + (15-.5x) + (60-2x) (Δx) (x) then simplified to get the work function = 81x-2.5x2dx 3. The attempt at a solution integrated work function 81x-2.5x2 over 0 to 30 and got 13950 ft/lbs total work.