One person can do a certain job in ten minutes, and another person can do the same job in fifteen minutes. How many minutes will they take to do the job together? If x represents how many minutes to do the job together, then how much of the job does the slowest person do?

Question

One person can do a certain job in ten minutes, and another person can do the same job in fifteen minutes. How many minutes will they take to do the job together?  If x represents how many minutes to do the job together, then how much of the job does the slowest person do?

anteater · Answer

So you need to first think about the rate at which each person does the job. The first person can do one job in ten minutes, so his rate of work is 1/10  job per minute.

What is the second person's rate?

anonymous · Answer

x

anteater · Answer

Actually, x represents the number of minutes it takes them to both complete the job.
But the second person can do the job in 15 minutes, so his rate of work is 1/15  job per minute.

anteater · Answer

So the first person can do one-tenth of a job per minute and the second person can do one-fifteenth of a job per minute. How would you  find their combined rate?

anonymous · Answer

yes

anteater · Answer

If the first one's rate is 1/10, and the second one's is 1/15, then if they were working together, how would you find their combined rate of work, do you think?

anteater · Answer

1/10 + 1/15 = ?