A word problem? How to set it up...thanks!

Question

anonymous · Answer

One pipe fills pool in 12 hours, second fills same pool in 3, when third pipe is added and all 3 are used, it take only 2 hours, how long does it take third pipe to do job alone

mysesshou · Answer

Maybe 
1/12 of volume per hour
1/3 of volume per hour
1/x of volume per hour
2hr
$$(\frac{1}{12}+\frac{1}{3}+\frac{1}{x})*Vol = 2hr$$
I think that might work.. .. i'd have to double check.

mysesshou · Answer

let me keep working on it.  something fishy.

anonymous · Answer

I got 2.4 is this right, you think?

mysesshou · Answer

i'm confusing myself.  How did you go about it?

mysesshou · Answer

1/12 V/h
1/3 V/h
1/x V/h

2 hours = 2/12 filled plus
2 hours = 2/3 filled plus
2 hours = 2/x filled
2/12 + 2/3 + 2/x = 1 = full
x=12
so the third pipe also fills pool in 12 hours.

$$Volume=1V=(\frac{1/12V}{hr}*2hr+\frac{1/3V}{hr}*2hr+\frac{1/x V}{hr}*2hr)$$
x=12
so the pipes are 12hr, 3hr, 12hr

to check:
   2/12+2/3+2/12
=2/12+8/12+2/12 =1 = the full volume

so the third pipe also fills pool in 12 hours.

I think this is it.