SOLUTION: Tom paints a fence in 4 hours.Huck paints the fence in 6 hours. How long does it take for them to paint the fence working together?

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Question 1041342: Tom paints a fence in 4 hours.Huck paints the fence in 6 hours. How long does it take for them to paint the fence working together?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Tom paints a fence in 4 hours.Huck paints the fence in 6 hours. How long does it take for them to paint the fence working together?
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Tom paints 1%2F4 of the fence length in one hour (in each hour).
It is his rate of work.

Huck paints 1%2F6 of the fence length in one hour (in each hour).
It is Huck's rate of work.

When the both work together, they paint 1%2F4+%2B+1%2F6 = 3%2F12+%2B+2%2F12 = 5%2F12 of the fence length in one hour. In each hour.

So, their combined rate of work is the sum of the individual rates and is equal to 5%2F12 of the fence length per hour.

It means that the both will complete their job in 12%2F5 of an hour.

1%2F5 of an hour is 12 minutes. 12%2F5 of the hour is 12*12 = 144 minutes, or 2 hours and 24 minutes.

Answer.  Both boys will complete the job in 2 hours and 24 minutes.

On solving joint work problems see the lessons
    - Rate of work problems,
    - Using Fractions to solve word problems on joint work,
    - Solving more complicated word problems on joint work,
    - Selected joint-work word problems from the archive
in this site.