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 = 1/2

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

This rate of work produces 2 hour/room.

2 hours