Tension in a Pulley System: Solving for Work Done by the Tension Force

[FizexAndStuff]

Homework Statement

Hi. My question is only regarding the early step in this problem that solves for tension. Here is the question:
"In a pulley system where masses m and M are connected by a rope over a massless and frictionless pulley, find the work done by the tension force in lifting mass m a distance h. Note that M > m and both masses are at the same height above the ground. The system is initially held at rest, and is then released."

Homework Equations

(T = tension, s = displacement)
W = F * s, here W = T*h

The Attempt at a Solution

So, I have already solved for acceleration of mass M and the v of m after it travels a distance h in another part of the problem, and I thought that I was fine with this one, but: I was summing forces to get the net force on m, which I thought would be T + (-mg) = ma. By following this, I said that T = ma + mg. That made sense to me because 'ma' is the net force, and 'ma' plus the amount of force subtracted by gravity is the total tension of the rope. However, when I finished the problem and checked it, the online review book said that Tension = mg - ma, and I am not sure why that is. Wouldn't that make Tension less than the force of gravity, and so mass m would go down instead of up?

 

[PhanthomJay]

The book may have made an error distinguishing between M and m.. You are correct that T = ma + mg.
It is also correct by looking at the forces acting on M that
T = Mg - Ma

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[FizexAndStuff]

Thanks. :)
I was worried that I was missing something important.