Here’s a very practical (and somewhat simplified) math problem that I was faced with today.

You’re deciding whether or not to take the bus or the subway. The stations are right next to each other, they cost the same amount of money, and they’re equally uncomfortable to ride. Suppose that the subway runs every five minutes, but you don’t know how often the bus runs or when the last bus came. Once you get on the bus, it only takes you 20 minutes to get to the destination. It takes 40 minutes by subway. You’re running late, so you want to minimize your travel time. If you’re really into economic details, assume you’re risk neutral and there’s no discounting.

Question 1: How do you figure out how long it’s been since the last bus came?

Question 2: What other piece of information do you need to figure this out exactly? (There are at least two acceptable answers here, but there may be more)

Question 3: Assume that piece of information is 30.  Do you take the bus or the subway?

Question 4: Wasn’t that fun?

If you see me standing at a bus stop, this is a good example of what I’m thinking about.

See the first comment for the answer!