Question: Hello:

How is the answer determined for the following?
If possible, use a simple calculation.

One worker can perform a certain job in 8 days, another worker in 10 days and a third worker in 12 days. In what time can all three perform it working together?

I believe that there is a basic or simple calculation that can be used, but I cannot determine what it is. I saw this question in an old textbook on arithmetic from the late 19th century. There are other "mind binding" questions from this book that I find interesting and challenging.

Would the solution be to add the days 8 + 10 + 12 and then divide by 3? This would equal 30/3 = 10 days.

I thank you for your reply and assistance.

Well, if the first worker can get it done on her own in eight days, then I'd be surprised to find that the group of them working together will take ten days to complete it. Let's look at work rates:

Worker A does the work at 1 job per 8 days which is one-eighth of a job per day.
Worker B does the work at 1 job per 10 days which is one-tenth of a job per day.
Worker C does the work at 1 job per 12 days which is one-twelfth of a job per day.

If you add the Rates, then you can get a team Rate:
1/8 + 1/10 + 1/12 = 15/120 + 12/120 + 10/120 = 37/120

That means they work at a rate that would get 37 jobs done in 120 days. Can you use this to figure out how many days it would take to get one job done?

Hope this helps,
Stephen La Rocque>