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Math Help - Distance problem

  1. #1
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    Distance problem

    A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?

    Equation: let x= walk rate
    \frac{32.4}{x}+\frac{32.4}{x+5.4}=12.6

    I think I set this equation up wrong...
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  2. #2
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    Re: Distance problem

    Quote Originally Posted by theloser View Post
    A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?

    Equation: let x= walk rate
    \frac{32.4}{x}+\frac{32.4}{x+5.4}=12.6

    I think I set this equation up wrong...
    it's set up correctly.
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  3. #3
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    Re: Distance problem

    Quote Originally Posted by skeeter View Post
    it's set up correctly.
    It ends up to be 12.6x^2-64.8x-106.92

    I then multiply every by 100 1260x^2-6480x-10692

    Then I factor everything by 36 (  35x^2-180x-297   )

    Then I can't factor the binomials... Must have done something wrong... help please. Thanks Thanks
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  4. #4
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    Re: Distance problem

    Quote Originally Posted by theloser View Post
    It ends up to be 12.6x^2-64.8x-106.92

    I then multiply every by 100 1260x^2-6480x-10692

    Then I factor everything by 36 (  35x^2-180x-297   )

    Then I can't factor the binomials... Must have done something wrong... help please. Thanks Thanks
    what makes you think the quadratic should factor? sometimes they don't. nothing is wrong ... break out your calculator and use the quadratic formula.
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  5. #5
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    Re: Distance problem

    You should have had

    32.4(x+5.4)+32.4x=12.6x(x+5.4)

    to start with.

    This gives eventually

    (7x+27)(5x-18)=0
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