SOLUTION: If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom work together to complete it?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom work together to complete it?      Log On


   

Question 203042: If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom work together to complete it?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes if all are working together
Then together they work at the rate of 1/x job per day
Sam works at the rate of 1/4 job per day
Lisa works at the rate of 1/6 job per day
Tom works at the rate of 1/2 job per day
So, together they work at the rate of 1/4 + 1/6 +1/2 =3/12+2/12+6/12=11/12 of the job per day. So, our equation to solve is:
11/12=1/x or
11x=12
x=12/11 days-----------------------amount of time when all are working together
In other words, just a bit over a day
Hope this helps---ptaylor