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Math Help - (1/(x+6))+(1/x)=(1/7)

  1. #1
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    (1/(x+6))+(1/x)=(1/7)

    Word Problem: Two companies working together can clear a parcel of land in 7 hours. Working alone, it would take Company A 6 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?

    This is what I did:
    Company A: x+6
    Company B: x

    Then it asked me to make an equation out of it. My answers we're all wrong, so I gave up and looked for the answer. And this is what they said:
    (1/(x+6))+(1/x)=(1/7)-capture.png
    ** Can somebody explain to me why the numerators are 1s?

    I got this far: x-8x-42=0
    Then, says I have to use the Quadratic Formula.
    Tried to solve it but I always end up with a radical.. which is: (82√58)/2
    and if simplified, would be (?): 4√58
    I re-checked several times but I cannot see what I did wrong..

    I appreciate any help.

    Thank You,
    Azusa.
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  2. #2
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    Re: (1/(x+6))+(1/x)=(1/7)

    Think of the amount done in 1 hour Together they do 1/7th of the work. The fraction A alone would in 1 hour is 1/x and for B it would be 1/(x+6)

    Hence together in 1 hour the fraction they would do would be 1/x+1/(x+6) which therefore =1/7
    Thanks from Azusa
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  3. #3
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    Re: (1/(x+6))+(1/x)=(1/7)

    Thank you, but do you happen to know the answer to the 2nd part of my question?
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  4. #4
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    Re: (1/(x+6))+(1/x)=(1/7)

    For the 2nd part I can't see anything wrong with your working. Only the positive answer applies of course.
    Thanks from Azusa
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  5. #5
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    Re: (1/(x+6))+(1/x)=(1/7)

    Quote Originally Posted by biffboy View Post
    For the 2nd part I can't see anything wrong with your working. Only the positive answer applies of course.
    Yep both +ve and -ve are correct ans for x - its just negative time doesn't make much sense to us.
    Thanks from Azusa
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