Question

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.

Answer 1

You cannot answer this without
making assumptions.

Hannah could help Destiny paint faster. For example fetching tools and food! In this case it could take less than 12 hours.

Hannah may be no help at all and Destiny does all the work and it takes 12 hours.

They could decide to paint exactly half the room each - that would take 10 hours.

However - I imagine that the question wants you to assume they work for the same amount of time - at these rates. In other words they both start painting from opposite sides of the room and stop when they meet then it would take

Time taken = 1 / rate

Per hour they paint 1/12 + 1/20 of a room = 10/120 + 6/120 = 16/ 120 = 2/15 of a room.

Time taken = 15 / 2 = 7.5 hours.

Answer 2

I believe it's 8 hours :)