Why is this the answer???

I can't for the life of me figure out why 2 2/5 is the answer to the following question. If anyone can explain this to me then I would appreciate it.

Question:

John can paint a fence by himself in 6 hours and Jenny can paint the fence in 4 hours. How long will it take them to paint the fence if they work together?

The answer is 2 2/5.

Re: Why is this the answer???

Quote:

Originally Posted by

**Runfast1** Question:

John can paint a fence by himself in 6 hours and Jenny can paint the fence in 4 hours. How long will it take them to paint the fence if they work together? The answer is 2 2/5.

$\displaystyle \frac{1}{6}+\frac{1}{4}=\frac{5}{12}$

So in one hour they can do $\displaystyle \left(\frac{5}{12}\right)^{th}$ of the fence.

THUS??

Re: Why is this the answer???

In 1 hour John alone can paint 1/6 of the fence and Jenny can paint 1/4 of the fence. So together in 1 hour they can paint 1/6+1/4 of fence. That is 5/12 of fence. So 1/12 of fence in 1/5 hour and whole fence (12/12) in 12/5 hours.

Re: Why is this the answer???

Thank you so much for the very quick help!