Sunday, May 25, 2008

Math puzzle: which station? (part 1)

Whoops, looks like I missed this week's regularly scheduled posting. It's late now and I don't feel like typing anything too involved, so here's a neat little math question I've been wondering about.

Environmentalist that I am (or "greentard," as my girlfriend likes to call me1), I like to take the T to work as often as I can. My 90-minute trek starts with a walk to the red line, which I take in to Park Street.2 There are two T stops, Porter and Davis, roughly equidistant from my house; the train going my direction hits Davis first, then Porter. The question is: does it matter which I take?

Here's my thinking. On the one hand, trains run through each station at the same pace, so it shouldn't matter where I wait. If I have to wait an average of X minutes at Porter, I should have to wait the same X minutes, on average, at Davis.

On the other hand, let's imagine that I walk to Davis and get there just in time to see the train pulling out; I missed it by 30 seconds. It takes a minute or two for the train to get to Porter, so if I'd instead gone to that station, I'd get there just before the train; perfect timing!

My hypothesis is that if my schedule and the trains' schedules were completely random, everything would even out and it wouldn't matter which station I went to. But neither one of them is totally random; the trains are relatively regular (every 7 or 8 minutes), and so am I (I try to leave around 7:45 am). If I assume that my time is somewhat synchronized with the trains' — with some randomization, since neither of us are flawless — I bet Porter is the better station. My time cost for being a bit ahead of the train isn't high (30 seconds or a minute), but if I'm a bit behind, I'll catch a train at Porter that I'd miss at Davis.

I'll run some simulations; stay tuned for the results next week.

Apologies if this post is badly written; the timestamp is my excuse.

[1] She stole this term shamelessly from Fake Steve Jobs.
[2] Sic. Remind me to write about my conundrum regarding "in to" and "into" soon.

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