SOLUTION: Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn th

Question 170686: Melanie can paint a certain barn by herself in x days. Her helper Melissa 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 Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Melanie can paint a certain barn by herself in x days. Her helper Melissa 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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This type of problem comes up in physical things, multiple pumps, electricity, maybe some others.
You find the reciprocal of the sum of the reciprocals.
In this problem, it's obvious that the time will be less than x days, so adding x and 2x is not the answer.
let T = the time working together.
1/T = 1/x + 1/2x
1/T = 3/2x
T = 2x/3, 16x hours.
It makes sense, it's less than either working alone, and between 1/2 of x and half of 2x.
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For x = 5
T = 10/3 days, or 3 days 8 hours. (3 24-hour days)
Again, that's between 2.5 and 5 hours, so it "looks right."

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