Question 231969: I have to write a rational expression for this word problem. Melanie can paint a barn in x days. Her helper Sara can paint the same barn in 2x days. Write a rational expression for the fraction of the barn that they can paint in 1 day by working together. Evaluate the expression for x=5.
Thanks,
Jim Koch
Answer by Robb(9)   (Show Source):
You can put this solution on YOUR website! If you're evaluating this for x=5, put the 5 in for the x's to give you the following rational expression:
1/5 + 1/(2*5) = 1/x
You only want one variable, x.
So assign x as the part of the barn they can paint together.
It takes melanie 5 days, so for one days work the fraction is 1/5.
It takes Sara twice as long, so 10 days. her work for 1 day is 1/10.
You don't know how long it will take them working together, so that portion is x
So you get the following equation:
1/5 + 1/10 = 1/x
The LCD is 10x, so multiply everything by 10x to give you:
2x + x = 10
Add like terms:
3x = 10
Divide both sides by 3:
x = 3 1/3 days
So it will take 3 and 1/3 days for them both working together to paint the barn.
You can check this by putting 3 1/3 in for x in our equation.
Hope this helps!
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