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

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
-----
Melissa DATA:
time = 2x days/job ; rate = 1/2x job/day
--------------------------
Together data:
time = t days/job ; rate = 1/t job/day
------------------
Equation:
rate + rate = together rate
1/x + 1/(2x) = 1/t
---
Solve for "t":
(2x+x)/(2x^2) = 1/t
---
t = (2x^2)/(3x)
t = (2/3)x
---------------------
t(5) = (2/3)5 = 3 1/3
============================
Cheers,
stan H.
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