### How Not To Miss The Bus

How Not To Miss The Bus

How not to miss the bus? This discussion seems to be stupid because a lot of people say that you will never miss the bus if you come to the stop on time. However, you will always miss your bus. The first reason is that you come to the bus stop a little late. The second reason is that you come too early and miss the earlier bus. The third reason is that the bus comes on irregular time. This means that you will always miss the bus. We are going to discuss this matter with mathematics.

Let’s suppose that your bus comes every ten minutes. This time, we will begin with a function y = x

y = the minutes of busees arriving in

x = the minutes of busses supposed to arrive in

The graph is lenear and the bus comes every ten minutes exactly.

If the bus is a little earlier, the function will be y = square root x and I’ll show you how it works.

The first bus will arrives in 3 minutes. The second bus will arrive in 4 minutes. The third bus will arive in 5 mihnutes. The fourth bus will arrive in 6 minutes. The fifth bus will arrive in 7 minutes. What this mean is that you will always miss the bus although you come early.

If the bus is a little late, the function will be y = x ln x and I’ll show you how it works.

The first bus arrives in 23 minutes. The second bus arrives in 60 minutes. The third bus arrives in 102 minutes. This means that the bus is always late and on irregular time.

Thinking of the functions I introduced above, bus is on time sometimes but also on irregular time often. When the bus is super early, the function will be y = square root x. When the bus is super late, the function will be y = x ln x, which means that it is nothing to do be early or be late.

Those three functions mentioned above tell you a mathematical lesson, which is a secant distant line. The medium of the secant distance and the medium of the x value between two x values are proportional, which means that the ideal time of being at the stop is between the previous bus and the next bus. Mostly, our buses in Victoria, BC come every 10 minutes, 15 minutes, or 20 minutes. What you do is to arrive the bus stop between the previous bus and the next bus.

By using a graphic calculator, you might see the secant distance between the first x value and the second x value. You will use a triangle formula for this: the secant distance D is the square root of xx + yy. Then, you can evaluate the ideal x value, which is the ideal time to be at the stop.

So, don’t just run to the bus stop or go there early and wait. If your bus comes at 3:00 p.m., you will need to go there at 2:55 p.m. with an assumption that the previous bus comes at 2:50 p.m. In that way, you will never miss the bus.

Thanks.

Alex Kim.