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Math Help - Work Problem

  1. #1
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    Work Problem

    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 fractions of the barn that they complete in one day by working together. Evaluate the expression for x = 5.

    I came up with this:

    Melanie = 1/x

    Melissa = 1/2x

    Together = 1/x

    1/x + 1/2x = 1/x

    What is the right set up?

    I can evaluate when x= 5. I just need the proper rational expression.

    Thanks


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  2. #2
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    Quote Originally Posted by magentarita View Post
    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 fractions of the barn that they complete in one day by working together. Evaluate the expression for x = 5.

    I came up with this:

    Melanie = 1/x

    Melissa = 1/2x

    Together = 1/x
    ??? Do you realize that you are saying that, working together, they work no faster than when Melanie works by herself? There is no "equation" here- you just want to add the two rates together to find how fast they work together. What is 1/x+ 1/2x ?

    And another thing- don't just write "Melanie= 1/x". The girl is not a number. Write "the rate at which Melanie paints the barn = 1/x". That makes it clear exactly what that number represents.

    1/x + 1/2x = 1/x

    What is the right set up?

    I can evaluate when x= 5. I just need the proper rational expression.

    Thanks


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  3. #3
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    Can you....

    Quote Originally Posted by HallsofIvy View Post
    ??? Do you realize that you are saying that, working together, they work no faster than when Melanie works by herself? There is no "equation" here- you just want to add the two rates together to find how fast they work together. What is 1/x+ 1/2x ?

    And another thing- don't just write "Melanie= 1/x". The girl is not a number. Write "the rate at which Melanie paints the barn = 1/x". That makes it clear exactly what that number represents.
    1/x + 1/2x = 3/2x

    If I then let x = 5, this is what I get:

    3/(2(5)) = 3/10 = 3/10

    What does 3/10 mean in this case?

    Is this correct?
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