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    sean080's Avatar
    sean080 Posts: 1, Reputation: 1
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    #1

    Dec 13, 2007, 12:09 AM
    Algebra Quadratic wordproblem
    Hi, I'm trying to figure this out but always have trouble with problems like this, here it is:

    Jennifer traveled at a constant speed on an old road for 160 miles. She then traveled 5 miles per hour faster on a newer road for 90 miles. If she drove for 6 hours, find the car's speed for the part of the trip that was traveled on the new road.
    jiten55's Avatar
    jiten55 Posts: 105, Reputation: 8
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    #2

    Dec 13, 2007, 03:56 AM
    Let speed on new road = x

    Original speed = x - 5

    Total time =

    160/(x - 5) + 90/x = 6

    Solve this equation to get value of x.
    asterisk_man's Avatar
    asterisk_man Posts: 476, Reputation: 32
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    #3

    Dec 13, 2007, 07:00 AM
    jiten55 is essentially correct. One extra thing to be aware of is that since this will result in a quadratic equation you'll end up with two mathematic solutions for x. However, only one of them will make sense with your problem, you should be able to figure out which one that is and discard the other.
    Shy But Nice's Avatar
    Shy But Nice Posts: 2, Reputation: 1
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    #4

    Dec 21, 2007, 07:40 AM
    so u feel x = 5.52631578947368
    jiten55's Avatar
    jiten55 Posts: 105, Reputation: 8
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    #5

    Dec 21, 2007, 08:27 AM
    Answer is 45.

    Reason:

    The quadraticd equation reduces to:

    3 x^2 - 140 x + 225 = 0

    It has roots: 45 and 10/3

    Only 45 is is valid, because (x -5 ) should not be negative.

    New Road: 45, Old Road = 40
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #6

    Dec 21, 2007, 08:31 AM
    Quote Originally Posted by Shy But Nice
    so u feel x = 5.52631578947368
    No, x is a nice integer solution. I will use r for rate.



    Multiply by the GCF, which is r(r+5):

    This results in a quadratic

    Factor:



    Which concurs with Jiten's post. Excellent.

    Of course, ignore the negative solution.

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