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

Question 217413: Melanie can paint a certain barn by herself in x days. Her helper Melisa 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 Melisa 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 paints 1/x of the barn per day.
Melisa paints 1/2x per day.
Together, they do 1/x + 1/2x per day
1/x + 1/2x = 3/2x per day.
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At x=5:
--> 3/10 per day.
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The long way for x - 5:
1/5 + 1/10 = 3/10 --> 10/3 days to paint the barn together
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A shortcut for x = 5: product/sum
5*10/(5+10) = 50/15
= 10/3 days
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