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Math Help - Help with Motion and distance word problems

  1. #1
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    Nov 2009
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    Help with Motion and distance word problems

    I am trying to figure out how to solve a distance question. I have the formula and the answer I just don't understand how to get to the answer and where to plug in my numbers. Can someone help me with this.

    Question:
    Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and jog was 2 minutes and 40 seconds. Find the length of the track.

    I have been trying to use the distance=(rate)(time)
    d=rt but I cannot get it to save my life.
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  2. #2
    MHF Contributor
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    Mar 2007
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    1,240

    Talking

    In future, please note that it will be much easier to help you locate your error(s) if you post what you've tried so far.

    What "distance" expression did you get for the first time, t, when he was running at r = 6?

    What "distance" expression did you get for the rest of the time, 160 - t, when he was jogging at r = 2?

    Since the distances were the same, what equation did you get? What solution did you get?

    Please be complete. Thank you!
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  3. #3
    MHF Contributor
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    Ottawa, Canada
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    Always useful if you set up a simple similar example:
    say 100 miles @ 50 mph takes 2 hours;
    returning @ 20 mph takes 5 hours.
    Play with that until you "see" what's going on...
    then apply what you've learned to your actual problem.
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  4. #4
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    Nov 2009
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    I got it

    since the distance was the same

    6t=2(160-t)

    6t=320-2t

    8t=320

    t=40 seconds

    6(40)=240 meters
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