Car Talk Puzzler

The other day I was listening to New Hampshire Public Radio when Car Talk came on. I ignored most of the show until the Puzzler appeared. Here is a transcript of what I heard.

RAY: I got this puzzler just recently from a young gal named Rosie Stephan. Time was of the essence, so I decided to use it. She writes:

Hi guys, my name is Rosie, and I'm 14 years old. My father Rich and I have been listening to your show every Saturday for .. well, as long as I can recall. Now, it is nearing the dreaded time in every father's life when his teenage daughter is about to turn 16. It's going to be hell and he knows it. So he's trying desperately to find a way to stall for time. This evening, he gave me this scenario: I can have my license at 16, if I can figure out the following problem.

So, obviously she's been unable to figure it out, so she's asking us, and if our listeners solve it, she's going to get her license.

TOM: That's not fair.

RAY: What do we care? All's fair in love and puzzlers! She continues,

My car's cooling system holds 12 quarts.

Note how she refers to it as "my car," and she doesn't even have her license yet!

Right now it has four quarts of antifreeze, and eight quarts of water. How much of this mixture do I have to drain out and replenish with straight antifreeze in order to get a 50/50 mixture? Please come to my aid. My life depends on it!

I thought I would add a "Part B" to this puzzler. How much of this mixture do I have to drain out if I'm adding antifreeze that's already been mixed 50/50 to get a 50/50 mix?

Can you solve these problems? They are kind of cute, and require nothing more advanced than high school algebra. You should try it yourself, before you look at the answer.

 
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Peter C. Scott
 
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