Expert: Ahmed Salami - 2/28/2006

Question
Hello:

One worker can perform a certain work in 8 days, a second worker in 10 days, and a third worker in 12 days.
In what time can the three men perform it working together?

If possible, try to solve this without using some advanced mathematical calculation.
There is a somewhat simple solution, but I cannot determine what it is.

I thank you for your reply.  

Answer
Hi,
Its a rate problem.
We simply determine how much work each worker can do in a day.
In a day, the first worker can perform 1/8 of the job. With similar arguments, the second and third workers can perform
1/10 and 1/12 of the work per day.
If they work together, they can perform(1/8 + 1/10 + 1/12) of the work in one day.
1/8 + 1/10 + 1/12 = 15/120 + 12/120 + 10/120
                 = 37/120
They can therefore perform 37/120 of the job in a day.
To complete the job, they'd need 120/37 days i.e in less than 4 days.
I hope it is clear.
Regards.