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**Tension and Pulleys....Cannot understand this problem**

So this is NOT for homework, (I'm doing practice problems reviewing for a final), but this is a textbook question that might as well be homework.

This is the question:

Figure 5-53 shows a man sitting in a bosun’s chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man’s hand. The combined mass of man and chair is 95.0 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity?

After looking at the solution, the part that confuses me is the 2T. I don't understand why 2T=mg+ma (m is the mass of the man-pulley) is the equation that we can use. Doesn't the tension cancel out so that mg=F, where F is the force of the hand pulling?

Thank you for taking the time to read this.