# How long does it take these boys to paint a fence?

I came across the following question:

If 3 boys can paint a fence in 2 days what part of the job can be completed by two boys in 1 day?

The answer to this problem is $\frac13$.

I can't manage to tackle this problem. Could anyone tell me what would be the quickest way to solve this problem (This question is a standardized test based question). Any help would be appreciated.

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Three boys paint it in two days. That means that it takes six times the amount of work a single boy can do in a day to finish painting (assuming every boy paints the same amount, of course); so one boy will take three times as long as three boys: six days. So in one day, a single boy can paint $\frac{1}{6}$th of the fence. Two boys will paint twice as much, that is $\frac{2}{6} = \frac{1}{3}$ of the fence.

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@ArturiMagidin Thanks for the explanation. So far I realize that 1 boy takes 6 days to paint. Could you explain how you got 1/6th of the fence ? –  Rajeshwar Jun 1 '12 at 3:31
@Rajeshwar: If it takes you six days to paint the whole fence, then how much fence are you painting each day? –  Arturo Magidin Jun 1 '12 at 3:33
Thanks. that helps.. –  Rajeshwar Jun 1 '12 at 3:34