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Math Help - Distance problem

  1. #1
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    Distance problem

    Carmen drove from Blairtown to Ore City, a distance of 80 miles. From Ore City she drove to Janesville, and the drove back to Blairtown. The ratio of Carmen's driving times on the first, second, and third segments of the trip, respectively, was 5:2:4, and she drove at the same average speed on each segment. What was Carmen's total driving distance, in miles, for the 3 segments of the trip?

    I know it is 176, but how do I show it algebraically?
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  2. #2
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    Re: Distance problem

    Hint: Since the average speed is the same, the ratio of distances is the same as the ratio of times. Indeed, let's say it took t_1 hours to drive from Blairtown to Ore City and t_2 hours to drive from Ore City to Janesville, and let the average speed be v. Then the distance between Blairtown and Ore City is vt_1 and the distance between Ore City and Janesville is vt_2. The ratio of these distances is \frac{vt_1}{vt_2}=\frac{t_1}{t_2}=\frac{5}{2} is the same as the ratio of times.
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  3. #3
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    Re: Distance problem

    Right, but how do i show it with 3 ratios?
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  4. #4
    Senior Member jakncoke's Avatar
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    Re: Distance problem

     \frac{5}{80} = \frac{2}{x} , x = 32 is the distance from Ore city to janesville.

     \frac{5}{80} = \frac{4}{x} , x = 64 is the distance from janesville to blairtown.

    so 64+32+80 = 176 is total driving distance
    Last edited by jakncoke; February 12th 2013 at 10:32 AM.
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  5. #5
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    Re: Distance problem

    Quote Originally Posted by jakncoke View Post
     \frac{5}{80} = \frac{x}{2} , x = 32 is the distance from Ore city to janesville.
    Hmm, there is something wrong about this proportion. I would say, 80 : x = 5 : 2 where x is the distance from Ore City and Janesville.
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  6. #6
    Senior Member jakncoke's Avatar
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    Re: Distance problem

    Quote Originally Posted by emakarov View Post
    Hmm, there is something wrong about this proportion. I would say, 80 : x = 5 : 2 where x is the distance from Ore City and Janesville.
    yes, i miswrote, i corrected it.
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