Coffee or tea?
I have a cup of tea and a cup of coffee. I take a teaspoonful of tea and add it to the cup of coffee; stir briskly; then take a teaspoonful of the mixture and return it to the cup of tea, and stir that briskly.
After I'm done, there is:
(a) more coffee in the teacup than tea in the coffee cup
(b) less coffee in the teacup than there is tea in the coffee cup
(c) exactly the same amount of coffee in the teacup as there is tea in the coffee cup
After I'm done, there is:
(a) more coffee in the teacup than tea in the coffee cup
(b) less coffee in the teacup than there is tea in the coffee cup
(c) exactly the same amount of coffee in the teacup as there is tea in the coffee cup
posted by Ross at
8:21 AM
19 Comments:
I'm pretty sure it's b, because once you've put the tea into the coffee, it's not all coffee. therefore the spoonful added to the tea is not all coffee and as such there is mostlikely less coffee in the tea as there is tea in the coffee
B.
The return mixture after the first blend is a diluted mix, and returning some part of tea to the tea cup.
"the spoonful added to the tea is not all coffee" -- correct, as far as it goes.
"The return mixture after the first blend is a diluted mix" -- correct, as far as it goes.
HOWEVER, B is still not the correct answer....
let's say one teaspoonful is 10% of a cup
then after the firstvdecanting there is 100% coffee and 10% tea = total of 110% in cup 1, witch is a ratio of 10:1 and 90% tea in cup 2
at the second decanting the first cup keeps the ratio of 10:1 and one teaspoon is 10 % of a full cup the teaspoon has 1/11th of the mixing in cup 1 wich is 9/110th(8.181818..% of a full cup) coffee and 1/110th tea(0.909090..% of a full cup).
so after the second decanting:
in cup 1(the one with coffee) is 10% - 0.9090..% = 9.0909..% tea
and in cup 2 (the tea cup) is 8.18181..% coffee
so the right would be b)
(but because i already this i know that the right answer must be c) so i made a mistake somewhere <.<)
i think i found it:
i forgot to subtract the 0.909090..% of tea in cup 1 at the second mixing from the 9.0909..% wich is 8.181818%, the same amount as coffe in the teacup.
I think that the answer is C, because the tea you have taken out of the mix to put back into the tea cup equals the amount of coffee left to replace it in the coffee cup. That's great english.
100 units Tea
Less 10 units (tea spoon)
100 units Coffee Plus 10 Units Tea
(Assumption)
110 Units Coffee/Tea Mix
Less 10 units (9 units Coffee/1 unit Tea ratio)
Leaves 91 units Coffee & 9 Units Tea
Tea cup then has 90 units Tea + 1 unit Tea and 9 units Coffee
They are the same. C
I assumed that the ratios of tea and coffee after the mix, and used a simplification for display purposes.
Correct, Carc! :-) C is the correct answer.
The neat thing is that this result doesn't depend on how big the cups are ... it doesn't even depend on the cups being the same size! Anyone want to prove that, using variables instead of distinct numbers?
Correct, Karl!
Instead of using 10 tablespoons use 9 so your fractions will be over 10. Easier to read.
9 tbs coffee and tea
take 1tbs from tea and add to coffee so 8tbs tea and 10tbs coffee
mix coffe and take tbs that 1 tbs (ratio 1/10 tea 9/10 coffee)
this leaves 8.1 tbs coffee and 0.9tbs tea
adding to tea (now 8 tbs) gives 8.1tbs tea and 0.9tbs coffee
Ross got it. And he's right, it doesn't matter how much tea or coffee there is.
I pinched this from a post that Wiz made.
"Just by logic. If you have the same volumes in each cup before and after then any amount of tea in the coffee must be matched by the same amount of coffee in the tea".
There is no need to do any calculations.
I wrote it! :-) Carc and Karl had the correct answers.
Hi Ross. My bad, I just assumed it was part of Zaux's blitz.
the blitz comment served its purpose :-)
ok here is the mathematic way with variables:
i made it as a chart, because it's easier to imagine
c = amount of coffee in cup 1
s = amount that fits in the spoon
t = amount of tea in cup 3
look here:
http://img39.imageshack.us/img39/4355/varchart.jpg
Hi Carc, I'm sorry but that's no good. e.g. What is C - (C+S)/C?
C is a volume, and (C+S)/C is a number. You can't do that.
Let C and T be the initial amounts of coffee and tea, and S be
the capacity of the spoon. Use [c] and [t] to keep a tag of the
ingredients.
The initial state is C[c] and T[t]. Transfer S[t] from the tea
cup to the coffee cup. Now coffee cup is C[c]+S[t] and the tea
cup is (T-S)[t]. Now transfer S from the coffee cup. S contains
S*(C/(C+S))[c] and S*(S/(C+S))[t]. That leaves the coffee cup with
(S - S*(S/(C+S))[t] and the tea cup now contains (CS)/(C+S))[c].
(S - S*(S/(C+S))[t] = S(1-S/(C+S))[t] = S(C/(C+S))[t]. Voila!
(CS)/(C+S)[t] in the coffee cup and (CS)/(C+S)[c] in the tea cup.
aargh you're right, i ignored the unit.
and i made a big mistake, because the (C+S)/C has to be CS/(C+S) (C/(C+S) for the concentration of coffee multipled with the volume of the spoon)
but if you change (C+S)/C to CS/(C+S) at my chart, you get the right conclusion
don't know how i got (C+S)/C, shame on me for that stupid mistake
The answer would be B
first off there are 2 cups one with coffee and the other with tea. One teaspoon of tea is put in the coffee (notice this is pure 100% tea). After it is mixed a teaspoon of the coffee (notice this is not pure tea) is placed back into the original cup.
100% > lesser%
therefore there is less coffee in the teacup than there is tea in the coffee cup
From The Godson
Hi Carc. I knew you'd kick yourself ;) It's surprising how easy it is to get into a muddle keeping track of what's going on. I must have made 3 or 4 silly slips before I finally posted.
Hi The Godson. You are right that pure tea is not returned to the tea cup, but pure coffee is not put in the tea cup either. The dilutions exactly compensate for each other.
Let s be the amount of tea moved from the tea cup to the coffee cup. Now take s by volume of the mixture. It will contain c+t = s (by volume). That will leave s-t tea in the coffee cup and add c = s-t to the tea cup. As s-t = s-t, each cup is equally contaminated (by volume).
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