Another Math Puzzle, But With Mushrooms!

Discussion in 'PHYSICS & MATHEMATICS' started by Terry M, Dec 3, 2012.

  1. Terry M

    Terry M Member Mushroom Doctor

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    OK, you're on an overnight mushroom-hunting trip which takes you up a mountain. You've heard that there is an enormous chaga mushroom at the top. You start up the mountain at 12 noon, and it takes you 4 hours to get to the top, which you therefore reach at 4 PM. It's getting dark, so you camp out overnight.

    You start going down the mountain the next day, beginning at the stroke of 12 noon once again. You take exactly the same route down, and it takes the same 4 hours. So it is again 4 PM when you are back where you started.

    Here's the question. Is there any moment when you pass exactly the same place at exactly the same time of day both going up and going down? Incidentally, you didn't find the chaga. :(
     
  2. RiverDweller

    RiverDweller Moderator Moderator Expert Identifier

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    so at 2pm, you should be in the same spot??

    I know that can't be right....lol
     
  3. LuckOfTheFryish

    LuckOfTheFryish Moderator Moderator Expert Identifier

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    im thinking the same thing RD...seems like right in the middle would be it but that also seems too obvious lol. hmmm.

    that sucks the chaga couldnt be found :(
     
  4. Professor PinHead

    Professor PinHead Lost in the Tek.... Administrator Mushroom Doctor Cannabis Doctor Supporter

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    I am guessing no......
    :spinningworld:
    The position of the planet changes therefore the time changes resulting in a change of coordinates on the way down in respect to time.
     
  5. Javadog

    Javadog Moderator Moderator Mushroom Doctor Cannabis Doctor

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    Ugh...yeah...imagine that you over-lapped the actions, with
    one you starting from the top and the other the bottom.

    It does seem that you'd meet in the middle, all other things
    being equal.

    I seem to prefer algebra. LOL

    JD

    P.S. We are having to take a lot for granted here, i.e. that the rate
    of ascent == rate of descent.
     
  6. Professor PinHead

    Professor PinHead Lost in the Tek.... Administrator Mushroom Doctor Cannabis Doctor Supporter

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    I was going to mention that too but didn't want to be too much of a bugger. :)

    The downward decent is always faster than the upward.

    Its a shitload more stress on your lower back and knees too...
     
  7. rogue

    rogue ♥ Hooked on Mycelium ♥ Moderator Mushroom Doctor Supporter

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    no one said it was straight up or straight down the mountain. :shrug:

    Not enought info :)
     
  8. LuckOfTheFryish

    LuckOfTheFryish Moderator Moderator Expert Identifier

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    yes but it does say it still takes 4 hours for the descent as well...

    and youre right prof...but it is also relative? i mean...technically no youre not really in the same place because of the movement of the earth but relative to the earth you can....so i mean it is possible as well. this question only raises further questions!

    given the info we have and assuming that place and time are relative to earth and using simply algebra wouldnt it be 2 PM youd be right in the middle?
     
  9. LuckOfTheFryish

    LuckOfTheFryish Moderator Moderator Expert Identifier

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    what about pee and snack breaks!!!?? omg overload. i need a cookie and some pudding.
     
  10. Javadog

    Javadog Moderator Moderator Mushroom Doctor Cannabis Doctor

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    I need a nap!
     
  11. RiverDweller

    RiverDweller Moderator Moderator Expert Identifier

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    this is bringing back flashes from high school when I was in math class reading my personal books, hidden of course by the big bulky textbook!
     
  12. Terry M

    Terry M Member Mushroom Doctor

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    You guys aren't looking at the question. It is:
    Is there any moment when you pass exactly the same place at exactly the same time of day.

    NOT
    Where or when do you pass exactly the same place at exactly the same time of day.

    Big difference! :)
     
  13. nomendubium

    nomendubium scraping by, since '97 Expert Identifier

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    algebra was my weakest math subject :(
    X(unknown distance) x R(unknown rate) =1/4 T(the time it took, 4 hours)
    XR=1/4T
    4xr=T
    4X=T/R
    12...1....2....3....4
    4....3....2....1...12
    strange, when I try to line up the times (taking into consideration 12 is 2 integers, and there for adding an extra dot to 4) they never do line up, even though there is the same amount of intigers and they start from the same place :confused:
    so I'm going to say no
     
  14. rogue

    rogue ♥ Hooked on Mycelium ♥ Moderator Mushroom Doctor Supporter

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    so does this mean at every point along the way? I feel very stupid. :(
     
  15. nomendubium

    nomendubium scraping by, since '97 Expert Identifier

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    lets try again, with each numeral or dot representing 15 minutes
    12..1...2...3...4
    4...3...2...1..12
    nope :( :)
     
  16. nomendubium

    nomendubium scraping by, since '97 Expert Identifier

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    IDK, I'm not smart, but it seems the only likelyhood would be near the middle of the trip and the 2's clearly don't line up.
     
  17. Terry M

    Terry M Member Mushroom Doctor

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    I'm going to post the answer at 9 pm EST, so as not to drive you crazy overnight.

    :outhair:
     
  18. LuckOfTheFryish

    LuckOfTheFryish Moderator Moderator Expert Identifier

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    oh ha. i say yes.
     
  19. Jeff

    Jeff Well-Known Member Moderator Mushroom Doctor Supporter

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    You can be in the same spot at the same time but not at the same moment.
     
  20. Terry M

    Terry M Member Mushroom Doctor

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    Here's the answer.

    There will always be one and exactly one time and place that will coincide for the trips up and down. It doesn't matter how fast or slow you go at any point. It's not necessarily at the middle, at 2 PM.

    It's not an algebra problem at all. There are no unknown numbers to figure out. Even though this is a math problem, there aren't any numbers in it.

    The secret is in looking at the problem the right way, which I think LuckOfTheFryish did. Here's how I like to see it. Imagine that you have one camera following you up the mountain, recording the 4-hour trip uphill. When you come down the next day, you record the 4-hour trip with another camera.

    You take the two cameras back home, and start playing the two recordings back, starting at the same time, on screens right next to each other. The left screen shows you starting at the bottom, at noon of the first day. The right screen has you start at the top at noon of the following day. The two playbacks are completely synchronized, so the same "time code" shows on both screens.

    Now, see how easy the answer is to get. As you watch the two screens, there is one thing that's unmistakable. As the two recordings play, the two "yous," the one going up and the one coming down, are coming closer together. As the playback continues, you come closer and closer. At the end of the 4 hours, you know that you will have to have crossed paths, at some place, at the same time. You don't know exactly where or when. But there has to be one place where it happens! And you'll be able to see that place on the synchronized playbacks.