Work Word Problem

[NJGx03x871]

Does this make it more clear for you?

If the first painter can do the entire job in twelve hours and the second painter can do it in eight hours, then (this here is the trick!) the first guy can do 1/12 of the job per hour, and the second guy can do 1/8 per hour. How much then can they do per hour if they work together?

To find out how much they can do together per hour, I add together what they can do individually per hour: 1/12 + 1/8 = 5/24. They can do 5/24 of the job per hour. Now I'll let "t" stand for how long they take to do the job together. Then they can do 1/t per hour, so 5/24 = 1/t. Flip the equation, and you get that t = 24/5 = 4.8 hours. That is:
hours to complete job:

first painter: 12
second painter: 8
together: t

completed per hour:
first painter: 1/12
second painter: 1/8
together: 1/t

adding their labor:
1/12 + 1/8 = 1/t

5/24 = 1/t

24/5 = t

They can complete the job together in just under five hours.

woah... do you have the same book? lol

that's almost verbatim the explanation given my my study booklet. Anyways, my question is why are we turning "t" into "1/t"...? logically it doesn't make sense to me.