Coffee or Tea?
Date: 07/09/2001 at 14:39:55 From: Traylor Subject: Mixtures Here is the problem: Person A has a cup of coffee. Person B has a cup of tea. Person A takes a teaspoon of coffee and puts it in the tea. Person B mixes the teaspoon of coffee and tea, then takes a teaspoon of the mixture and returns it to the coffee. Is there more coffee in the tea, or more tea in the coffee, or are they the same? My thought is there is more coffee in the tea. I have been told they are the same. Could you please explain this, because I don't get it!
Date: 07/09/2001 at 18:03:43 From: Doctor Rob Subject: Re: Mixtures Thanks for writing to Ask Dr. Math, Traylor. They are the same. The volume of each cup after the swap is the same. That means that whatever coffee is missing from the first cup must have been replaced with exactly the same amount of tea. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
Date: 07/16/2001 at 17:39:18 From: Doctor Ian Subject: Re: Mixtures Hi Traylor, Suppose I have a school full of boys, and a separate school full of the same number of girls. I fill a bus with boys, drive them over to the girls' school, and let them mingle. Then I grab enough boys and girls to fill the bus, and drive them back over to the boys' school. Now, are there more girls at the boys' school, or more boys at the girls' school? Do you see why I could have accomplished the same thing by filling the bus with boys, driving over to the girls, telling _some_ of the boys to get off, and picking up enough girls to take their places? When you think about it this way, it becomes pretty obvious that every boy who goes over to the girls' school is replaced by one girl who goes back to the boys' school. In your problem, the teaspoon leaves the coffee cup full of some amount of coffee. When it comes back, some of the coffee has been replaced with tea. How much tea comes back? One unit of tea comes back for each unit of coffee left behind. This is a problem that has driven a lot of people crazy over the years. You can a very extensive description of it here: Brain teaser: the wine in the water problem - Donald Sauter http://www.geocities.com/CapitolHill/lobby/7049/wine.htm Focusing on mixtures in this context can be a red herring. Mixtures are something that most people don't have a lot of experience with, so they get caught up in trying to reason about what's happening when two things get mixed, which leads them away from the solution, rather than toward it. I hope this helps. Write back if you have more questions, about this or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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