Let be R the surface of the room ;
In an hour, Hannah paint R / 9 of the room ;
In an hour,Destiny paint R / 12 if the room ;
In an hour, Hannah and Destiny paint R / 9 + R / 12 = 4R / 36 + 3R / 36 = 7R / 36 of the room ;
They paint the room ( R ) in 36 / 7 = 5 1 / 7 hours ≈ 5 hours and 9 minutes ;