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Optimization Train Problem

  1. Jun 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A train leaves the station at 10:00 and travels due south at a speed of 60 km/h. Another train has been heading due west at 45 km/h and reaches the same station at 11:00. At what time were the two trains closest together?

    2. Relevant equations

    3. The attempt at a solution
    The trouble I am having is the wording of the question. I think it means the trains left from two different stations and will arrive at the same time together at one station. So the equation for that scenario is:

    [tex]f(t) = \sqrt{(60-60t)^{2}+(45t)^{2}}[/tex]

    However I get a range outside the limit of one hour. I think I'm just confused about he wording if someone can clarify it for me. Any help is appreciated.
  2. jcsd
  3. Jun 15, 2008 #2


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    Hi Delber! :smile:

    It means train 2 arrives at the same station one hour after train 1 left. :smile:
  4. Jun 15, 2008 #3
    Thanks for the clarification.

    So the new equation should be:


    Edit: Yep, I get the correct answer in the book. Thanks for the help.
    Last edited: Jun 15, 2008
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