Simple math - Lynyrd Skynyrd

Here is a little math problem we might do. It requires a diagram: ‘Here you are; the x represents you. And here’s your classmate, who we’ll draw as a y. You’re right next to each other when we start the observation; obviously you’ve had to walk to get there, too, and from different paths, but we aren’t interested in that right now. We’re taking just that situation, between when you’re right here, to when you get to class, over here. C marks the spot. The squares are all buildings; you can go into them, or you can walk around them. Everyone come up to the board, up, make a line, and draw some of the different paths you could take from where you are to C. (They draw, some straight, some looping.)

Okay, lots of different ways. Which are the fastest, do you think, and the slowest? Remember, they’re only the best in this situation if that’s what the question’s asking for, the fastest. (Erases all but two after the discussion). So let’s say x—that’s you—goes this way; y, your classmate, she goes this way. Which one gets to class first? (Same.) What if I said, you walk at 3mph and she walks at 5mph? (y). But what if I want to know exactly how long it takes each of you, how much sooner she arrives? Do we need to know something else? (the distance, if only in terms of units). What relationships do we know between distance, speed and time? (m/h; v=d/t, rearrange, convert units)

Now, what does this tell us? It gives us some useful information, right? We know what time class starts, and we don’t want to be late—maybe we also don’t want to be too early; since you and your classmate decide not to walk together, you probably won’t talk sitting waiting for the teacher, either. But what doesn’t this tell us? Well, we can imagine some more things to add to the problem, like weather, and hills, that we could factor in. It doesn’t tell us why x walks slower—is it cause you’re sad and drag your feet? Is it cause you’re happy and enjoy the walk? Of course no one goes exactly 5mph, either—that’s an average, an approximation—what do these words mean again? (it takes a generalization of moments; it is close to reality.)

Now, I’m basing this problem on an experience of mine, when I would walk to class this way and see someone else go this way, and the reason I bring it up is because there is something else that happened that we could in one sense factor in but that, again, would only tell us part of the story. I saw my friend because he was coming out of the building and walking up this way (b). Even though we didn’t stop to talk, and I didn’t slow or speed up or swerve enough to affect the problem, it made me smile. Isn’t that important? And who or what did I miss by not going another way?