Work problem: 12 min for one person, 18 min for another

[Motherof8]

It takes one person 12 minutes to do a job, another perspn 18 minutes. How long would it take for both of them to do the job together?

I figured 12 minutes is 1/5 of an hour(60 minutes) and 18 minutes is 3/10 of an hour. 1/5 = 2/10. 2x/10 + 3x/10 =10/10 or 1. 10/1 X 5x/10 =5x. 10 X 10 =100. 5x = 100. x= 20 minutes, but the answer in the back of the book was 7 1/5 minutes. How did I figure it wrong? I know that with 2 people wprking it should take less time.

[vribli]

Assume a job is x.
In 12 minutes, person A does x, and in 18 minutes, person B does x too.

So, we'll view it in 1 minute.
In 1 minute, essentially person A does x/12 minutes and person B does x/18 minutes. So if A and B does it together they do x/12 + x/18 of work.

Simplifying the denominator, we we'll get 5x/36 right?
Now to do x, we need to get the time.

So, x/(5x/36)=x(36/5x) = 36/5 = 7.2 minutes!

All done!

Hope you understand my workings!