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Math Help - Need help setting up Optimization problem

  1. #1
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    Need help setting up Optimization problem

    Any hints on how to set up the function for this problem?

    A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/hr. Another boat has been heading due east at 15 km/hr and reaches the same dock at 3:00 pm. At what time were the two boats closest together?

    From the question, I know that I have to minimize the distance between the boats, which can be obtained using the pythagorean theorem or distance formula. But that's about all I can think of.
    Anyone have any idea on how to set the equation using those speeds?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Arturo_026 View Post
    Any hints on how to set up the function for this problem?

    A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/hr. Another boat has been heading due east at 15 km/hr and reaches the same dock at 3:00 pm. At what time were the two boats closest together?

    From the question, I know that I have to minimize the distance between the boats, which can be obtained using the pythagorean theorem or distance formula. But that's about all I can think of.
    Anyone have any idea on how to set the equation using those speeds?

    Thanks in advance.
    let t = 0 be 2:00 PM and the port be the origin

    1st boat position ...

    y = -20t

    2nd boat position ...

    x = -15 + 15t

    let r = distance between the two positions at any time t ...

    r^2 = (-20t)^2 + (-15+15t)^2

    minimize r^2 w/r to time and you minimize r
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  3. #3
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    Ok, I get t=9/25 as the time when the boats are closer, but since the time goes from 2:00 pm to 3:00 pm, do I subtract those 21 min. 35 sec. from 3:00 or add them to 2:00?
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  4. #4
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    Quote Originally Posted by Arturo_026 View Post
    Ok, I get t=9/25 as the time when the boats are closer, but since the time goes from 2:00 pm to 3:00 pm, do I subtract those 21 min. 35 sec. from 3:00 or add them to 2:00?
    t = 0 is 2:00 PM

    what does that tell you?
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