Hannah can paint a room in 9 hours. Destiny can paint the same room in 12 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.

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;