My Life In Algebra

Remember those early algebra problems where one train leaves a station going 60 miles per hour and the other leaves its station going 40 miles per hour and you have to figure out where they will meet?

Yesterday morning, I had to meet someone at 8. It was too far to walk, but I had time to walk some of it. So I got on the bus at 7:30 and was trying to figure out where to get off so that I could walk as much as possible and still be there at 8. I knew it was 13 minutes from where I used to live, and about half an hour from where I used to work, which meant I should get off somewhere between the two, but I didn't know how long it would take the bus to get from where I used to work to where I used to live. And then I realized it was one of those algebra problems!

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OK, I kept writing this post as follows.

If X equals distance traveled and Y equals distance walked, bus speed times (X minus Y) plus walk speed times Y equals 30 minutes. Otherwise known as B(X-Y) + WY = 30

Only I didn't know the distance, bus speed, or walk speed, so I got off where I used to live and was early.

Then I posted it, reconsidered, and wrote.

If X = distance, Y = distance walked, and Z = time walked, X = Y times Z plus 30 minus Z times X minus Y. Otherwise known as X = YZ + (30-Z)(X-Y).

Only that doesn't seem right, because I need the speed. So I tried again.

If X equals distance, Y equals distance walked, and Z equals time walked, bus speed times (X-Y) equals 30 minus Z AND walk speed times Y equals Z. Otherwise known as BS(X-Y) = (30 - Z) and WS(Y) = Z.

Since I have two equations, I can solve for two variables (right?). To solve for Z (time walked) and Y, I would need to know the same variables as above: distance, bus speed, and walk speed (which is what those old train problems always gave you).

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This was my original conclusion.

I'm actually a huge believer in the value of algebra, both mathematically and in relation to higher order thinking (see Algebra Project), but I'm afraid the real-life application in this case was solely theoretical.

I would still hold to that, but I would add that I can see why people find algebra frustrating, even though I quite enjoy it. And I'm also wondering whether I look like a total idiot here for screwing up or at least over-complicating reasonably simple math..