paul paints a room in 6 hours. joel paints the room in 3 hours. how long will it take them to paint togather?

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 = 1/2Together, they can paint at the rate of 1/2 room/hour .This rate of work produces 2 hour/room.

[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