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# There are two glasses on the table, one containing water and the other one milk. They both contain exactly the same amount by volume. If you

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There are two glasses on the table, one containing water and the other one milk. They both contain exactly the same amount by volume. If you take a teaspoon of water and mix it into the milk and then take a teaspoonful from the milk glass and mix it with the water, both glasses become contaminated. But which is the more contaminated? Does the water now contain more milk than the milk does water or the other way round?

May 16, 2015

#1
+111470
+13

I'll give this one a try  !!!!

The volumes in the glasses don't really matter since they're the same......and the amount we put into each glass doesn't matter, either.......as long as it's the same...

Suppose there are 9 teaspoons of each liquid in each glass.

Taking a  tsp of water and putiing it into the glass of milk results a mixture of milk and water that is 9 parts milk and 1 part water.  {We assume this is well-mixed !!! }  Also, there are now 8 tsp of water left in the pure water glass.

Now taking a tsp of the water/milk mixture and putting it into the pure water glass results in a mixture of 8.1 tsp water and .9 tsp milk....a 9 : 1 ratio

But....the original pure milk glass now contains 9 tsp of the water/milk mixture....and 9 parts of this is milk (8.1 tsp) and 1 part is water (.9 tsp)

So......each glass is equally contaminated......the original pure milk glass contains .9 tsp of water and 8.1 tsp of milk.....a 1 : 9 ratio

And the original pure water glass contains .9 tsp of milk and 8.1 tsp of water....again, a 1 : 9 ratio.

May 16, 2015

#1
+111470
+13

I'll give this one a try  !!!!

The volumes in the glasses don't really matter since they're the same......and the amount we put into each glass doesn't matter, either.......as long as it's the same...

Suppose there are 9 teaspoons of each liquid in each glass.

Taking a  tsp of water and putiing it into the glass of milk results a mixture of milk and water that is 9 parts milk and 1 part water.  {We assume this is well-mixed !!! }  Also, there are now 8 tsp of water left in the pure water glass.

Now taking a tsp of the water/milk mixture and putting it into the pure water glass results in a mixture of 8.1 tsp water and .9 tsp milk....a 9 : 1 ratio

But....the original pure milk glass now contains 9 tsp of the water/milk mixture....and 9 parts of this is milk (8.1 tsp) and 1 part is water (.9 tsp)

So......each glass is equally contaminated......the original pure milk glass contains .9 tsp of water and 8.1 tsp of milk.....a 1 : 9 ratio

And the original pure water glass contains .9 tsp of milk and 8.1 tsp of water....again, a 1 : 9 ratio.

CPhill May 16, 2015
#2
+111246
+5

I really like your explanation here Chris!

They will both be equally contaminated!