SOLUTION: It takes Tom 2 days to paint a house and it takes Leah 4 days and it takes Lisa 6 days. How long will it take to paint the house together? Please explain how to set up this soluti

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Question 122248: It takes Tom 2 days to paint a house and it takes Leah 4 days and it takes Lisa 6 days. How long will it take to paint the house together?
Please explain how to set up this solution
Found 2 solutions by stanbon, jainenderkapoor:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
It takes Tom 2 days to paint a house and it takes Leah 4 days and it takes Lisa 6 days. How long will it take to paint the house together?
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Tom DATA:
Time = 2 day/job ; Rate = 1/2 job/day
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Leah DATA:
Time = 4 day/job ; Rate = 1/4 job/day
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Lisa DATA:
Time = 6 day/job ; Rate = 1/6 job/day
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Together DATA:
Time = x day/job ; Rate = 1/x job/day
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EQUATION:
rate + rate+ rate = together rate
1/2 + 1/4 + 1/6 = 1/x
Multiply thru by 12x to get:
6x + 3x + 2x = 12
11x = 12
x = 12/11 = 1 1/11 day (time needed to do the job together)
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Cheers,
Stan H.

Answer by jainenderkapoor(61) (Show Source):
You can put this solution on YOUR website!
It takes Tom 2 days to paint a house and it takes Leah 4 days and it takes Lisa 6 days.
We find one day work of each
Tom's 1 day work = 1/2 of the work
Leah's 1 day work = 1/4 of the work
Lisa's 1 day work = 1/6 of the work
1 day work of all the three = 1/2 + 1/4 + 1/6 = 11/12 of the work.
11/12 work is finished in = 1 day
1 work will be finished in 1/(11/12) = 12/11 = 1 1/11 days
Hope the solution is clear to you. If you need any help, I am available for Online Tutoring at very reasonable rates. My email is is jainenderkapoor@gmail.com