Question 14582: What is the general way of doing these?
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?
0.8 days
1.09 days
1.23 days
1.65 days
1.97 days
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! One way to do these kinds of problems is to find the rate at which each person works. In this case, you find the rate (portion of the job per day) for each of the three participants and add them together to find the rate (portion of the job per day) of the combined team.
Knowing how much of the job can be done in one day, you find the total time, in days, by inverting the rate.
If Sam can do the job in 4 days, then he can do 1/4 of the job in 1 day.
If Lisa can do the job in 6 days, then she can do 1/6 of the job in 1 day.
If Tom can do the job in 2 days, then he can do 1/2 the job in 1 day.
Now you have the daily rate of each of the participants. To find their daily rate if they work as a team, just add the individual daily rates.
 = 11/12
The team can do 11/12 of the job in 1 day.
It would take them 12/11 days to complete the job.
12/11 days = 1.09 days.
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