work rate problem. GMAT -related I'm looking for a good formula/system to use for these problems. Too often I'm just relying on raw intuition and it takes me too much time to solve these questions. Is there a good starting place to solve these problems? What's like a good step 1 and step 2?
Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
So I don't know a good way to start. I thought output = rate * time but what is it here?
Let me think....
So rate * time = output. Okay. What else? Well, rates add onto each other without synergy... this is an assumption about rate problems on the GMAT. So if Machine A completes a 1/12 of a job in 1 hour and machine B completes 2/12 of a job in 1 hour, the two machines combined complete 3/12 of a job in 1 hour.
Is it 6 * r * 12 = 1
72r = 1
r = 1/72??
Why does that makes sense? Can I just arbitrarily make the job = 1?
So 1/72 is the rate of 1 machine.
x * 1/72 * 8 = 1
x = 9
So the answer is 9-6 = 3
What's a good way to think about this? 
Someone, in a not very helpful way, suggested multiplying 6 * 12... but that doesn't explain to me what to do.
The answer is 3.

Any time you have multiple machines working together, you add their rate to get the total rate.  In this case, the machines all have the same rate, so their total rate for the 6 machines is just 6r.  We know that rate*time=work, so we know that 6r*12days=W (W can represent the  job they complete)
Now we want to know how many more machines need to be added to complete the job in 8 days.  We can represent that like this xr*8days=W.  I find it easier to start by just making it x then subtracting the 6 later to avoid additional needless computation. 
since, they are both completing the same job, we know that xr*8=6r*12 and solve for x
x=9, once we subtract the original 6 we get our answer 3
