Finding the acceleration of gravity given 2 masses

[jg871]

Homework Statement

We are given 2 hanging masses on opposite sides of a pully. masses and distance traveled in the time are given. We are required to find the acceleration of gravity

Homework Equations

m1 (g+a)=m2 (g-a)

The Attempt at a Solution

I found acceleration and have now changed weights w1 and w2 equal to m1g+m1a and m2g-m2a. I am having trouble solving for g. Could I get some help on how I do this? The answer is 9.7m/s^2 but do not know how to isolate g.
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[BiGyElLoWhAt]

Where did that equation come from?

 

[jg871]

Where did that equation come from?

I'm not entirely certain where the instructor whipped it out but This is what equations have came up with the problem thus far:
T(tension)-w1=m1a which can be turned to T=m1a+w1 which can be turned to T=m1a+m1g. This would be the same case for w2-T=m2a. Then the equation m1g+m1a=m2g+m2a was written down and we were told we could find g from there

 

[gneill]

Your Relevant equation is fine. It seems that you're having an algebra problem, not a physics problem

Why not start by expanding both sides of your m1 (g+a)=m2 (g-a) expression, then gather all the terms containing g on one side and the rest on the other side of the equal sign?

 

[jg871]

m1g-m2g=m2a-m1a? Would I then factor out the g?

 

[gneill]

m1g-m2g=m2a-m1a? Would I then factor out the g?

You've lost the sign of the m2a term on the right hand side. It didn't change sides, so it must retain its original sign.

Yes, you then factor out the g and isolate it.