Question

One custodian cleans a suite of offices in 3 hours. When a second worker is asked to join the regular custodian, the job takes only 2 hours. How long does it take the second worker to do the same job alone?

Answer 1

6 hours

Explanation:

Let x represent the time in hours it takes the second worker to do the job alone. Then each hour, 1/x of the job gets done by that worker. Similarly, the regular custodian accomplishes 1/3 of the job in each hour. Working together, they do 1/2 of the job each hour:

1/3 +1/x = 1/2

1/x = 1/2 -1/3 = 3/6 -2/6 = 1/6 . . . . subtract 1/3 and simplify

x = 6

It takes the second worker 6 hours to do the same job alone.