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Question 445982: 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 Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! 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?
Make this chart
no. of jobs done time in days rate in jobs/day
Sam
Lisa
Tom
All 3
Let x be the time it takes all of them to complete the job.
Fill in the other given times:
no. of jobs done time in days rate in jobs/day
Sam 4
Lisa 6
Tom 2
All 3 x
In all four cases exactly 1 job was done, so we fill in the
number of jobs in every case as 1:
no. of jobs done time in days rate in jobs/day
Sam 1 4
Lisa 1 6
Tom 1 2
All 3 1 x
Now we fill in the rates in jobs/day by dividing the number of
jobs by the number of days required to complete it:
no. of jobs done time in days rate in jobs/day
Sam 1 4 1/4
Lisa 1 6 1/6
Tom 1 2 1/2
All 3 1 x 1/x
Now that the chart is filled in, we use the fact that the sum
of the individual rates equals to the rate of all 3 working
together, so
1/4 + 1/6 + 1/2 = 1/x
Solve that by multiplying through by the LCD of 12x
Answer: 12/11 = 1 1/11 days
Edwin
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