Robert can paint a room in 6 hours. Julio can paint a room in 8 hours. how long will it take for the two of them to paint a room together?

Robert paints 1/6 of a room in an hour.

Julio paints 1/8 of a room in an hour.

Working together, they can paint (1/6 + 1/8) room/hour =

(4/24 + 3/24) room/hour =

7/24 of a room per hour.

7/24 of a room per hour means

24 hours / 7 rooms =

(24 / 7) (hour/room) = (3 and 3/7) hour per room.

1/6+1/8=1/x

1/6 * (6*8*x) + 1/8 (6*8*x) = 1/x (6*8*x)

8x+6x=48

14x=48

divide each by 14

x=48/14

x = 3.43 roughly