This afternoon, while riding the subway, I noticed an ad that the MTA has been running for some time now as part of its self-promoting “SubTalk” campaign. It reads:
In 1986, the subway and bus fare was $1. That’s $1.89 in 2008 dollars. Today, 30-day Unlimited Ride MetroCard brings the fare down to $1.17. Believe it.
Maybe I’m a crotchety windbag, or maybe the afternoon’s chatter with friends about the GRE mathematics section sparked something off, but I didn’t, as the ad implored me to, believe it. Assuming that the ad campaign was started before the subway fare increase earlier this year that raised the base fare to $2.25 from its previous $2, it seemed like the MTA was taking a pretty liberal view of how many times one would have to ride the subway or bus with their monthly MetroCard to bring their effective fare down by 30%.
(In case you’re not familiar with how the 30-day MetroCard works, you can pay a flat fee per month for unlimited use of the New York subway and local buses instead of the pay-per-ride fare)
Partly to prove that I could still actually do arithmetic and basic algebra (and render it in TeX), I scribbled out this calculation:
I’m sure this broke all sorts of mathematical conventions, but p_m is the price of a 30-day card, p_r is the effective per-ride cost according to the MTA, and r, r_d, and r_w are rides per month, day, and week, respectively you’d need to make to get that price.
This assumes the 2008 30-day fare of $81. To get the purported $1.17 fare, you’d have to ride the subway or bus (not including free transfers) about 2.3 times per day, every day, or just over 16 times per week, for the entire 30-day period. I have no idea where the MTA got their data from, but I don’t know anyone who rides the subway that much.