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John, Paul and Peter can finish painting the fence in 2 hours. If John does the job alone he can finish it in \(6\) hours. If Paul does the job alone he can finish it in \(8\) hours. How long will it take for Peter to finish the job alone?

 Feb 12, 2022
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Suppose Peter can finish painting the fence in x hours. That means he can paint 1/x of the fence in 1 hour, John can paint 1/6 of the fence in 1 hour, and Paul can paint 1/8 of the fence in 1 hour. We can write the following equation:

 

1/6 + 1/8 + 1/x = 1/2

 

Solving, we get x = 24/5, so it takes Peter 24/5 hours to paint the fence alone.

 Feb 12, 2022

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