Question

I know the answer to this problem, but I don’t know how to get the answer:

It takes you and your sister 3 hours to clean the entire house when you work together. If you can do the job alone in 4 hours, how long would it take your sister to do it by herself?

Answer 1

12 hours

Explanation:

For problems like this, it works well to think in terms of jobs per hour, rather than the given hours per job.

When you both work together, your rate is 1/3 job per hour. When you work alone, your rate is 1/4 job per hour. Then the rate increase that is contributed by your sister is the difference of these rates:

(1/3 job/h) - (1/4 job/h) = (1/3 -1/4) job/h = 1/12 job/h

If your sister can do 1/12 of the job in 1 hour, then it takes her 12 hours to do the entire job by herself.