Answer :

konrad509
[tex]\frac{1}{6}+\frac{1}{3}=\frac{1}{x}\\ \frac{1}{6}+\frac{2}{6}=\frac{1}{x}\\ \frac{3}{6}=\frac{1}{x}\\ \frac{1}{2}=\frac{1}{x}\\ x=2[/tex]

2 hours
AL2006
Paul paints 1/6 of the room each hour.
Joel paints 1/3 of the room each hour.

Working together, they paint (1/6 + 1/3) of the room each hour.

In order to add the fractions, you need a common denominator.
6 will work:

(1/6 + 1/3) = (1/6 + 2/6) = 3/6 = 1/2

Together, they can paint at the rate of 1/2 room/hour .

This rate of work produces 2 hour/room.

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