Question

One custodian cleans a suite of offices in 3 hrs. 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

The regular custodian's cleaning rate is 1/3 suites per hour. The combined cleaning rate is 1/2 suites per hour. The combined cleaning rate is (rate 1) + (rate 2) = 1/2 rate 2 = 1/2 - 1/3 = 3/6 - 2/6 = 1/6 The second worker's rate is 1/6 suites per hour. Therefore, the second worker can do the same job alone in 6 hours.