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generis
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I had to think about this one for a second rather than jumping in blindly and using equations.

If Lindsay painted 1/x the room in 1 hour, then we know that Joseph painted 1 - 1/x of the room in one hour.

This means that in 20 minutes, he painted a third of his total in 1 hour:

1/3 x (1 - 1/x)
= (x - 1)/3x
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Assuming the total work required to paint a wall = W.

The rate of work of Lindsay = L, the rate of work of Joseph = J.

Given Lindsay completes \(\frac{1}{x} \)of total work in 1 one hour = \(L\left(1\right)\ =\ \frac{W}{x}\)

Lindsay and Joseph combined can complete the entire work in one hour: \(\frac{W}{x}+\ J\ =\ W\)

Hence J = \(W-\ \frac{W}{x}=\ \frac{W\left(x-1\right)}{x}\)

Hence Joseph completes \(\frac{\left(x-1\right)}{x}\) part of the work in an hour.

In 20 minutes he will be completing a third of this work : \(\frac{\left(x-1\right)}{3x}\)
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Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

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