You can go to the site, but here is the pertinent information -
- Participants will begin running at 4 AM.
- The catcher car will take off 30 minutes later, initially going just under 10 miles per hour.
- Gradually, the catcher car will increase speeds throughout the race and pursue runners form behind.
- Once the catcher car passes an individual, that marks their personal finish line.
This is a little like the infamous "A trains leave Omaha, with another train leaving an hour later..." type of problem. Those problems are kind of pointless, though. All you really care about is when your train gets in, and that is solved by just looking it up online.
This one is more fun. If you are in the race, you really would want to do some math ahead of time to plan your strategy. The car gradually speeds up. Since we don't know how much, let's just assume it stays at 10 mph. If so, running at 10 mph or faster means we won't ever get caught. (There are runners that could go a long way at that pace. However, if the car just picks it up to 16 miles per hour, it is going at world record mile pace.)
Suppose you are running at a very respectable 8 miles per hour for "t" hours. The car is moving at 10 mph for "t-0.5" hours. Since distance = rate x time and we want to see when the car catches you (i.e., the distances are the same), we have the equation, 10(t-0.5) = 8t. Solving the equation gives t = 2.5 hours. Depending on how fast the car speeds up, you will be caught sometime within 2 hours, 30 minutes.
It seems to me there are quite a few interesting problems the potential runner could come up with if he/she was going to compete in this race. Such as: When will you get caught if you go 7 mph; how fast do you have to run to not get caught for an hour; what happens if the car goes 2 mph faster every half hour? I'll leave that to you to consider.
