I don't have a bike

The amount of thoughts that go through my head in a day cannot simply be expressed in the limited "What's on you mind" box on Facebook. So I made a blog. It was far easier than I imagined, and its free too! Anyways, this blog is really going to be about weird things I wonder when I'm walking home from campus. They aren't always deep, but they are interesting to me.

Today, after finishing my torturous online math assignment with a friend on campus, he got on his bike, and I started to walk home. I fumed internally about how I can't ride a bike (legitimate reasons, don't worry) and wondered if two people could get somewhere together faster with only one bike. (no double riders, bike reconstruction,  etc.). Well my curious mind found out that that was incredibly easy compared to the math I was just doing 5 minutes ago, and yes, you can get there faster together on one bike, you just have the guy on the bike ride halfway and drop the bike and start walking. The other guy would reach the bike on foot and ride it to the end, where the now walking person would arrive at the same time. (assuming equal biking speeds and walking speeds) This is true because both individuals cover the same distances in the same amount of time, just in a different order.

But what if there were 3 people and one bike? Easy. Each would travel 1/3 the distance on the bike, and the rest on foot. This gets a little useless if the amount of people gets absurdly large, but it increases their travel time as an entire group. You can visualize this pretty easily too. The first biker rides out to 1/n of the distance. (n=#of travelers) and drops the bike. The next biker (in a group of walkers at the same distance) picks up the bike and travels to the 2/n mark, where he will meet the first biker exactly. This continues until the last biker rides the bike to meet the group of (n-1) walkers at n/n (the end). It's so cool! (to me anyways) I know there's a way to describe the ratio of time saved for any of these if I know the difference in the bike's velocity and the walker's velocity. But I'm too lazy to figure it out.

I don't always think about math, but today certainly isn't an exception. :D