Help Calculus 2 work problems, I can't set up the equation properly.
A leaky 10 kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope that weighs 0.8 kg/m. Initially the bucket contins 36kg of water but the water leaks at a constant rate of finishing draining completely when it reaches the 12 m. How much is the work done?

I did work of cable = F * D, F = mass * (any height)
= 0.8(12-x),

then work Bucket is
(0,46), (12,0) and came up with the equation from the slope of -3x +46. I added those together to get

w total: = Integral of 0.8(12-x)+(-3x+46) dx

Question

Help Calculus 2 work problems, I can't set up the equation properly.
A leaky 10 kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope that weighs 0.8 kg/m. Initially the bucket contins 36kg of water but the water leaks at a constant rate of  finishing draining completely when it reaches the 12 m.  How much is the work done?

I did work of cable = F * D, F = mass * (any height)
= 0.8(12-x),

then work Bucket is 
(0,46), (12,0) and came up with the equation from the slope of -3x +46. I added those together to get

w total: = Integral of 0.8(12-x)+(-3x+46) dx

jotopia34 · Answer

$$W total = \int\limits_{0}^{12}0.8(12-x)+(12-x)(-3x+46)dx$$

jotopia34 · Answer

If anyone in the world ever looks at this, my error was in not multiplying by gravity, of 9.8

jotopia34 · Answer

I get a star