Three electricians are wiring my new home. Electrician 1 by himself will need 11 days to do the job. Electrician 2 will need 5 days to do the job, and electrician 3 by himself will need 9 days. If all three electricians work on the same job together how many days will it take them to complete the job?
Work problems are quite interesting - and sometimes counterintuitive. The key is to remember that the group will be faster than any of them working alone.
Here is the solution.:
Electrician 1 can complete 1/11 of the job in one day
Electrician 2 can complete 1/5 of the job in one day
Electrician 3 can complete 1/9 of the job in one day
So working together, they can complete (1/11)+(1/5)+(1/9) in one day
We need to add the three fractions, so we need a common demoninator. It's 11X5X9=495
So (1/11)+(1/5)+(1/9) =(45/495)+(99/495)+(55/495)=199/495
199 is prime so this fraction cannot be reduced further, so they can, indeed do 199/495 of the job in one day.
As a result, it will take them 495/199 days , or 2 97/199 days to do the job, or approximately 2 days, 11 hours, and 42 minutes