Hannah can paint a room in 20 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.

16, because if they both do half, 12/2=6 and 20/2=10 10+6=16. I hope that this is correct.

(Corrected the Answer :p )

Hannah can paint the room in 20 hours. So each hour, Hannah paints 1/20 of the room.
Destiny can paint the room in 12 hours. So each hour, Destiny paints 1/16 of the room.
In 1 hour, both of them can paint 1/20 + 1/16 = 4/80 + 5/80 = 9/80.

As you noticed before, proportion painted in 1 hour and the total time to paint the whole room were inversed. Same thing for both of them.
They both paint 9/80 of the room in 1 hour. So to paint the whole room, they take 80/9= 8.9 hours (80/9 inverse of 9/80).

Hope this Helps! :)