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Math Help - Word problem on quad. equation

  1. #1
    Junior Member
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    Exclamation Word problem on quad. equation

    on a journey of 250 km, a driver calculated that by increasing his average speed, by 5 km/h, he would take 25 minutes less. find his usual average speed , correct to 2 dec. places.

    Ans: 52.33 km/h

    i really need to know how to get this answer- i've tried by forming the quadratic equation:

    250 - 250 = 25
    x (x+5) 60

    by keeping the speed as x.

    pls help!
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  2. #2
    MHF Contributor
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    Talking

    What you've posted is actually a rational equation.

    What did you get when you solved this equation?

    Please be complete. Thank you!
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  3. #3
    Member
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    \frac{250}{x} - \frac{250}{x+5} = \frac{25}{60}

    \frac{250}{x} - \frac{250}{x+5} = \frac{5}{12}

    remove the denominators
    \frac{250}{x} - \frac{250}{x+5} = \frac{5}{12} ] (12)(x)(x+5)

    <br />
(250)(12)(x+5) - 250(12)(x) = 5(x)(x+5)

    3000x + 15000 - 3000x = 5x^2 + 25x

    15000 = 5x^2 + 25x

    5x^2 + 25x - 15000 = 0 (then simplify by dividing by 5)

    x^2 + 5x - 3000 = 0<br />

    Then I used the quadratic formula:


    x = \frac{-5 +  \sqrt12025}{2}

    and

    x = \frac{-5 -  \sqrt12025}{2}

    For the addition:

    x = \frac{-5  - 109.66}{2}

    x = \frac{104.66}{2}

    x = 52.33

    For the subtraction: REJECTED

    x = \frac{-5  - 109.66}{2}

    x = \frac {-114.66}{2}

    x = -57.33 (REJECTED)
    Last edited by reiward; September 28th 2009 at 05:47 PM.
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