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Math Help - weird one

  1. #1
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    weird one

    I got a good one. You have a cup of tea and a barrel of whiskey. You take one teaspoon full of tea from the tea cup and you put it in the whiskey. You then take the tea spoon out and then you put it back in the barrel of whiskey (the one thats filled with some tea now) and then take one teaspoon and you put it in the tea cup, so now the tea cup has some whiskey in it. Now the question is, is there more whiskey in the tea cup or is there more tea in the whiskey barrel?
    please explain your answer
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by nertil1 View Post
    I got a good one. You have a cup of tea and a barrel of whiskey. You take one teaspoon full of tea from the tea cup and you put it in the whiskey. You then take the tea spoon out and then you put it back in the barrel of whiskey (the one thats filled with some tea now) and then take one teaspoon and you put it in the tea cup, so now the tea cup has some whiskey in it. Now the question is, is there more whiskey in the tea cup or is there more tea in the whiskey barrel?
    please explain your answer
    I think there is equal quantity of tea in barrel and whiskey in cup.

    I thought that there is one teaspoon in both of them, but I think when you put teaspoon filled from whiskey barrel to cup you have returned also some tea to cup. So lets say that teaspoon contains 99% whiskey and 1% (previously puted) tea so you have again same quantity of tea and whiskey because you have left 99% tea of teaspoon in barrel and you have puted 99% whiskey of teaspoon in cup.

    Hope this makes sense...
    Last edited by OReilly; November 12th 2006 at 01:57 AM. Reason: Typo
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  3. #3
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    Hello, nertil1!

    Another classic problem . . .


    You have a cup of tea and a barrel of whiskey.
    You take one teaspoon of tea from the cup and you put it in the whiskey.
    You then take one teaspoon of the mixture and put it in the tea cup.

    Is there more whiskey in the tea cup or is there more tea in the whiskey barrel?
    Code:
                          *               *
                          |---------------|
                          |///////////////|
                          |///////////////|
                          |///////////////|
          *           *   |///////////////|
          |-----------|   |/// Whiskey ///|
          |:::::::::::|   |///////////////|
          |:::::::::::|   |///////////////|
          |::: Tea :::|   |///////////////|
          |:::::::::::|   |///////////////|
          *-----------*   *---------------*

    Since one teaspoon of liquid is removed from the cup
    . . and then one teaspoon of liquid is replaced in the cup,
    both containers have their original amounts of liquid.

    Some amount of whiskey is now in the teacup;
    . . we don't know exactly how much.

    But we do know that that amount of whiskey
    . . displaces an equal amount of tea, which is now in the barrel.
    Code:
                          *               *
                          |---------------|
                          |::::: Tea :::::|
                          |---------------|
                          |///////////////|
          *           *   |///////////////|
          |-----------|   |/// Whiskey ///|
          |/ Whiskey /|   |///////////////|
          |-----------|   |///////////////|
          |::: Tea :::|   |///////////////|
          |:::::::::::|   |///////////////|
          *-----------*   *---------------*

    QED . . . The amounts are equal.

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  4. #4
    Forum Admin topsquark's Avatar
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    I can't give you rep for that one, but it was very nicely explained!

    -Dan
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  5. #5
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, nertil1!

    Another classic problem . . .


    Since one teaspoon of liquid is removed from the cup
    . . and then one teaspoon of liquid is replaced in the cup,
    both containers have their original amounts of liquid.

    Some amount of whiskey is now in the teacup;
    . . we don't know exactly how much.

    But we do know that that amount of whiskey
    . . displaces an equal amount of tea, which is now in the barrel.[/size]
    QED . . . The amounts are equal.

    [/size]

    My explanation is little scrapy but it's the same as yours in principle.

    AND I POST IT FIRST!!!!
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  6. #6
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    Here's analytic proof they are equal.

    Assume for simplicity that a teaspoon is size s, a cup is size cand a barrel is size b.
    The total volume of cup and barrel is c+b.

    Call the units of tea t and units of whiskey w.

    Before anything is done, things look like this:
    Cup: ct.
    Barrel: bw.

    After moving one teaspoon from the cup to the barrel:
    Cup: ct-st=(c-s)t.
    Barrel: bw+st.

    The volume of the barrel is now b+s. The substance in the barrel (which is a mixture of whiskey and tea) is \frac{bw+st}{b+s}, derived by taking a barrel of whiskey and a teaspoon of tea, and dividing this amount by one barrel plus one teaspoon.

    This resolves to \left(\frac{b}{b+s}\right)w+\left(\frac{s}{b+s}\ri  ght)t since this format conforms better to amount of whiskey plus amount of tea.

    Now we move a teaspoon from the barrel to the cup.

    The cup contains: ct-st+s\left[\left(\frac{b}{b+s}\right)w+\left(\frac{s}{b+s}\ri  ght)t\right]
    and the barrel contains:
    bw+st-s\left[\left(\frac{b}{b+s}\right)w+\left(\frac{s}{b+s}\ri  ght)t\right].

    Clearly there is \frac{sb}{b+s} amount of whiskey in the cup, and there is s - \frac{s^2}{b+s} = \frac{sb}{b+s} amount of tea in the barrel.
    They are the same.
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  7. #7
    Senior Member TriKri's Avatar
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    Quote Originally Posted by nertil1 View Post
    I got a good one. You have a cup of tea and a barrel of whiskey. You take one teaspoon full of tea from the tea cup and you put it in the whiskey. You then take the tea spoon out and then you put it back in the barrel of whiskey (the one thats filled with some tea now) and then take one teaspoon and you put it in the tea cup, so now the tea cup has some whiskey in it. Now the question is, is there more whiskey in the tea cup or is there more tea in the whiskey barrel?
    please explain your answer
    Well, after you have finished moving tea and whiskey forth and back, there should be totaly as much in both the cup and the barrel as there was from the begining. That means that as much whiskey it is in the tea cup, as much tea is missing from the tea cup. And that tea is in the barrel. So therefore it is as much tea in the barrel as there is whiskey in the cup.
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