SOLUTION: 90. Barn Painting. 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 f
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Question 347673: 90. Barn Painting. 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 stanbon(75887) (Show Source):
You can put this solution on YOUR website! Barn Painting. 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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Melanie DATA:
time = x day/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 = t days/job ; rate = 1/t job/day
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Equation:
rate + rate = together rate
1/x + 1/(2x) = 1/t
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Solve for "t":
(2x+x)/(2x^2) = 1/t
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t = (2x^2)/(3x)
t = (2/3)x
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t(5) = (2/3)5 = 3 1/3
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Cheers,
stan H.
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