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?

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(20055) (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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