The Bus Route Problem

For this blog I chose to write about the bus far problem. I like this problem because many people get it wrong just by guessing. It seems so simple and obvious as to what the answer is and many people are surprised to find that they are wrong. Just to test this, I showed both of my parents this problem. Not surprisingly, they both answered wrong after thinking about the problem for a few short seconds. As I explained it to them, I felt my understanding of the problem and what makes it so interesting grow. What the problem does is that it measures two separate things. As the diagram shows, you have a far greater chance (over half) of showing up to the station during the 35 minute interval. So to many  people, especially those waiting for a bus, it would seem that the average time for the bus to arrive was between 20 and 30 minutes. But this is not what the question is asking. If you average all the times on the diagram out, it comes to a perfect 15 minute interval between buses. So in fact, this bus service is indeed doing their job and buses are arrival at 15 minutes on average. My parents got quite the kick out of this one :)