Person A can complete a job in 6 hours. Person B can complete the same job in 4 hours. Working at the same rate, how many hours will it take both of them to complete the job?

Answer: it will take both of them 2.4 hours to complete the job.

Step-by-step explanation:

Person A can complete a job in 6 hours. This means that the rate at which Person A can complete the job per hour is 1/6

Person B can complete the same job in 4 hours. This means that the rate at which Person A can complete the job per hour is 1/4

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/6 + 1/4 = 5/12

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

5/12 = 1/t

t = 12/5

t = 2.4 hours