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Math Help - Confusing Word Problem

  1. #1
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    Confusing Word Problem

    Ok so ive been playing around with this, and i think its pretty simple...but i just cant figure it out. A worker can cover a parking lot with asphalt in 10 hours. With the help of an assistant the work can be done in 6 hours. How long would it take the assistant working alone to cover the parking lot? The answer i got was 12...because if they are both working for 6 hours, and they cover it, that is 6 hours of work each splitting the job, so if the assistant does both halves of the work, he would have worked for 12 hours. Please help, lemme know if im doing it wrong.
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  2. #2
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    The first guy covers \frac{1}{10} parking lots per hour, (imagine like miles per hour)

    The speed at which the other guy does a parking lot is \frac{1}{x} parking lots per hour

    Together they work at a speed of \frac{1}{6} parking lots per hour

    So it comes out to: \frac{1}{10}+\frac{1}{x}=\frac{1}{6}

    Let's multiply everything by 30x to get: 3x+30=5x

    Subtract 3x from both sides: 30=2x\quad\rightarrow\quad 2x = 30

    Divide by two: x = 15

    So the partner works at a rate of \frac{1}{15} parking lots per hour, so it takes him \boxed{15 \text{ hours}} to do the job alone.
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  3. #3
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    wow i was totally wrong on that one, thx for explaining that, your awesome
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