Question

Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?

2.4 hours
2.5 hours
3.0 hours
4.0 hours

The answer is supposedly 2.4 hours, but how ?? Please explain. Thanks!

Answer 1

In one hour Randy cleans at least 1/4 of the offices and in one hour Trey cleans at least 1/6 of the offices.

Working together they would clean at least 1/4 + 1/6 = 5/12 of the offices.

Let x be the greatest amount of time it would take them to clean the offices together. Then we can write the following equation:

5x/12=1