SOLUTION: Intermediate and Elementary Algebra 3rd Edition ISBN: 9780073533490 6.4 Exercise: 90 Melanie can paint a certain barn by herself in X days. Her helper Melissa can paint the

Question 260237: Intermediate and Elementary Algebra 3rd Edition
ISBN: 9780073533490
6.4 Exercise: 90
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!
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.
-----------------
Melanie DATA:
time = X days/job ; rate = 1/X job/day
-----------------------
Melissa DATA:
time = 2X days/job ; rate = 1/2x job/day
-------------------------------------------
Together DATA:
time = k days/job ; rate = 1/k job/day
----------------------------------------------
Equation:
rate + rate = together rate
1/x + 1/2x = 1/k
(2x+x)/2x^2 = 1/k
---
k = 2x^2/(3x)
k = (2/3)x (# of days it takes for them to do the job working together)
----
If x = 5
# of days = (2/3)5 = 10/3 = 3 1/3 days
===========================================
Cheers,
Stan H.
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