SOLUTION: Melanie can paint a certain barn by herself in xday. her helper Malissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that

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Question 126772: Melanie can paint a certain barn by herself in xday. her helper Malissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x=5.
Answer by stanbon(75887) About Me  (Show Source):
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Melanie can paint a certain barn by herself in xday. her helper Malissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x=5.
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Melanie DATA;
Time = x days/job ; Rate = 1/x job/day
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Melissa DATA:
Time = 2x days/job ; Rate = 1/2x job/day
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Together data:
Time = k days/job ; Rate = 1/k job/day
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EQUATION:
rate + rate = togther rate
1/x + 1/2x = 1/k
3x/2x^2 = 1/k
k = 2x^2/3x = (2/3)x
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If x = 5 the two will require (2/3)5 = 10/3 = 3 1/3 days to do the job.
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Cheers,
Stan H.