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 worked 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 worked together to complete it?       Log On


   

Question 166866: 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 worked 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 three are working together
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
Together, they work at the rate of 1/4 +1/6 +1/2 =
3/12 +2/12 +6/12=11/12 job per day, so our equation to solve is:
(11/12)*x=1 (1 job, that is) multiply each side by 12
11x=12 divide each term by x
x=12/11 days=1.09 days-----time it takes if all three are working together
CK
Sam: (1/4)(12/11)=3/11
Lisa: (1/6)(12/11)=2/11
Tom: (1/2)(12/11)=6/11
3/11+2/11+6/11=11/11
1=1
Hope this helps---ptaylor