Acceleration of block/pulley system

1. The problem statement, all variables and given/known data
What is the acceleration of the 2.0 block in the figure across the frictionless table?
Hint: Think carefully about the acceleration constraint.
I've attached the diagram.

2. Relevant equations
F=ma


3. The attempt at a solution
A=1.0kg block
B=2.0kg block
For block A: mAa1=2T
0=-Fg+n
For block B: mBa2=T-Fg
and no forces in x direction

So I assume the tension is equal because it is the same string. I also assume that the accelerations are different for the blocks though I'm not completely sure what to assume/why. All I really need is an explanation as to what I should know about the acceleration and why that is.

 

Oh okay, that makes sense. Thanks a lot!