Bad Dog brain teaser!

Discussion in 'Bad Dog Cafe' started by Junkyard Dog, Mar 13, 2019.

  1. PlainAllman

    PlainAllman Tele-Meister

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    1 mile
     
  2. Steve 78

    Steve 78 Tele-Afflicted

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    I got 1.618, but it was doing my head in so could be wrong.
     
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  3. Scottz

    Scottz Tele-Holic

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    1.25 miles
     
  4. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    Not 1.618 and not 1.25.
     
  5. Jupiter

    Jupiter Telefied Silver Supporter

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    Hang on, are you asking how far he walked or how far he ADVANCED?
     
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  6. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    How far the messenger walked...i.e. messenger walked some distance on the way to the rear of the column, then walked some distance (possibly different) on the return to the front of the column, and add those two distances up.
     
  7. Shuster

    Shuster Tele-Afflicted Silver Supporter

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    This is easy, just not seeing it??
     
    Last edited: Mar 14, 2019
  8. HoodieMcFoodie

    HoodieMcFoodie Doctor of Teleocity Ad Free Member

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    2.414213562 miles, give or take.
     
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  9. Brad Pittiful

    Brad Pittiful Doctor of Teleocity Ad Free Member

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    he walked one column...he stood at the front and waited till the back got to him...them he went back to the front
     
  10. Mouth

    Mouth Tele-Holic

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    I'm saying 1.
     
  11. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    This is the correct answer!
     
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  12. boneyguy

    boneyguy Doctor of Teleocity

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    That's what I immediately thought..BUT....you have to remember that when the messenger is walking to the rear the column is moving forward, toward the messenger...so that's going to be less than one mile.....and the reverse would be true when the messenger turns around and walks toward the front.....right? Maybe?
     
  13. Larmo63

    Larmo63 Tele-Afflicted

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    P O T A T O.
     
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  14. Jupiter

    Jupiter Telefied Silver Supporter

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    Exactly, so why doesn’t it balance out? I dunno.

    EDIT: nevermind!
     
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  15. Jupiter

    Jupiter Telefied Silver Supporter

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    A silver star for you!
     
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  16. boneyguy

    boneyguy Doctor of Teleocity

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    So, how do you arrive at the answer......what's the solution? Or am I simply a pawn in an elaborate hoax!!
     
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  17. Chunkocaster

    Chunkocaster Friend of Leo's

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    I'd also like to know how you arrived at that calculation and why I didn't win with my 2 and a bit answer.:)
     
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  18. Danocoustic

    Danocoustic Tele-Meister

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  19. Bones

    Bones Telefied Ad Free Member

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    Me I would stand in one spot wait for the last guy and then double time the mile up to the front and walk only one mile.
     
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  20. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    Here's the way I did it. First write down an equation for the time, t1, that it takes for the messenger to walk from the front of the column to the rear:

    t1 = L/(Vm + Vc)​

    L represents the column length, given to be 1 mile. Vm and Vc represent the constant paces of the messenger and the column...these are not known, but that is ok.

    Similarly, the time, t2, for messenger to walk from the rear back to the front is given by:

    t2 = L/(Vm - Vc)​

    Then the total time, t, for the messenger to walk from the front to the rear and back to the front is just the sum of t1 and t2:

    t = L/(Vm + Vc) + L/(Vm - Vc)​

    Now, it is important to note that during this total time, the column has covered it's legnth, so then:

    Vc = L/t​

    The previous two equations may be combined and rearranged to this familiar form of a quadratic equation:

    Vm^2 - (2*L/t)*Vm - (L/t)^2 = 0​

    Solve the quadratic equation and simplify to get two possible solutions:

    Vm = L/t +/- (L/t)*sqrt(2)​

    Here sqrt(2) is shorthand for the square root of 2, or 1.414. But Vm must be greater (or messenger could not possibly ever make it back) than Vc, which is also L/t (from a few equations previously), therefore the only solution can be:

    Vm = L/t + (L/t)*sqrt(2)​

    This equation can be rearranged to give the total distance walked by the messenger, which is simply the messenger's pace multiplied by the time:

    Vm*t = L*(1 + sqrt(2)) = 2.414*L​

    And for L = 1 mile, this is 2.414 miles.
     
    Last edited: Mar 14, 2019
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