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Math Help - College Algebra word problem help

  1. #1
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    Talking College Algebra word problem help

    First time posting so here goes. Would like to know how to solve.

    1. It takes Jake 10 hrs to paint a house. When his friend Betty helps it takes 6 hours to paint the same house. How long does it take for betty paint the house alone?



    2. A carpet amnufacturer blends 2 fibers one 20 percent wool and the second 50 percent wool, how many pounds of each fiber should be woven to produce 500lbs that is 35 percent wool?




    Thanks
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  2. #2
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    For the first one, think about how much they can do in one hour and together. If it takes, for example, 4 hours to do a job, then in one hour you can do 1/4 of the job, right?

    So, in one hour, Jake can do 1/10th of the job. Betty can do 1/x of the job (i.e., she can do the whole job in x hours.) If they work together they can do 1/6 of the job. Another way of representing the hourly amount they can get done when working together is simply to add 1/10 + 1/x.

    This gives \frac{1}{10} + \frac{1}{x} = \frac{1}{6}. Using 30 as a common denominator:

    \frac{3}{30}+\frac{1}{x}=\frac{5}{30} -->

    \frac{1}{x} = \frac{2}{30} = \frac{1}{15}, so x = 15.

    ---

    #2)

    Let's say he uses x pounds of the 20% wool fiber. Then the amount of wool fiber from that type of cloth or carpet or what-have-you is (.20)*x.

    Now, if he used x pounds of the 20%, he must use 500-x of the 50% fiber (since he used 500 pounds total). The wool from the 50%-type can be expressed, then, as (.50)(500-x).

    We also know that the total wool in the final, 500 pounds can be written as (.35)*500.

    If we take the wool from the 20%, add it to the wool from the 50%, it should equal the wool in the 35% mixture.

    This gives:

    .2x + 250 -.5x = 175.

    Solving for x gives 250. So he uses 250 of one fiber, 250 of the other.

    This makes sense since 35% is exactly halfway between 20 and 50. Thus, he should use half of each.
    Last edited by Mathnasium; February 28th 2008 at 01:37 PM.
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  3. #3
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    Wow thanks for the quick reply
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