What is the work done on a bucket hanging in a well?

[enian]

Homework Statement

An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00m.
(a) How much work do you do on the bucket in pulling it up?
(b) How much work does gravity do on the bucket?
(c) What si the total work done on the bucket?

The Attempt at a Solution

I couldn't get part (a). I may not be understanding it right.
I said..
W = F d
W = (9.8*6.75) * 4.0m
W = 264.6 J
*assuming by slowly they mean the upward force is just slightly more than the weight

but the answer in the back of the book for a is 3.6J??

 

[Littlepig]

i guess the book is wrong..3.6 J to pull a 6.75kg 4meters... not even in the moon would be that work...

 

[enian]

Is my method right though?