Final answer:
It would take approximately 6 hours and 51 minutes for both Raquel and Kylie to paint the room if they are working together.
Step-by-step explanation:
To find out how long it takes for both Raquel and Kylie to paint the room together, we can calculate their combined work rate by adding up their individual work rates. Raquel can paint the room in 12 hours, so her work rate is 1/12 of the room per hour. Kylie can paint the room in 16 hours, so her work rate is 1/16 of the room per hour. To calculate their combined work rate, we add up their individual work rates: 1/12 + 1/16 = 4/48 + 3/48 = 7/48. Therefore, their combined work rate is 7/48 of the room per hour. To find out how long it would take for them to paint the room together, we can divide the total work (which is 1 room) by the combined work rate. So, 1 / (7/48) = 48/7 = 6 6/7. Therefore, it would take approximately 6 hours and 51 minutes for both Raquel and Kylie to paint the room if they are working together.