To determine how many hours it takes Kent and Kendra to paint the room when working together, we can calculate their combined work rate.
Kent can paint the room in 6 hours, which means his work rate is 1 room per 6 hours (1/6 rooms per hour).
Kendra, on the other hand, can paint the same room in 4 hours, so her work rate is 1 room per 4 hours (1/4 rooms per hour).
To find their combined work rate, we can add their individual work rates:
1/6 + 1/4 = (2/12) + (3/12) = 5/12
Therefore, when Kent and Kendra work together, their combined work rate is 5/12 rooms per hour.
To calculate the time it takes them to paint the room together, we can use the formula:
Time = 1 / Combined work rate
Time = 1 / (5/12) = 12/5 = 2.4 hours
Therefore, it takes Kent and Kendra approximately 2.4 hours to paint the room when they work together.