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Wednesday, August 5, 2009

Math Problem

As part of a rather odd driving challenge you are required to complete two laps of a racetrack at an overall average speed of 80mph.  

At the instant you finish the first lap, you are informed that your average speed over that first lap was only  40mph.  

How fast do you need to travel over the second lap to get your overall average speed up to the target value of 80mph?

(Hint: it is harder than you might think)


Carolyn said...

After I finish working on this, can I steal it and give it to my math students? At the moment I'm trying to "justify" my guess and check method with some math logic.I find it interesting that "guess and check" seems to be a gut instinct even for me, the math teacher. Then I back into how to logically (systematically?) explain what I tried. This actually is a good problem for some "collaborative" work.
I was reading a couple of your recent posts. Interesting. I also liked very set rules and "how to" as a math student. I actually think more conceptually now that I have to teach. It's interesting.

Carolyn said...

Oh no, I can't believe I'm going to confess that I'm stumped to the whole world. My gut keeps telling me that if you covered half the distance at half the speed you wanted to, that you can't go fast enough to recover. And now that I have that stuck in my head, I'm not going anywhere.... I keep guessing and checking with the same type of reasoning... Ok, I'm headed off to the math faculty office to pass this along to some of the other teachers. I hope they don't look at me and say "duh"! No, they won't do that. They're not like that. Someone help me out here!...