Will I ever be able to Time Travel?

The faster that I travel, the less time it takes for me to arrive someplace. So when I move faster I can subtract time. So how fast will I have to go in order to arrive before I leave (i.e. When will time become a negative value)?

This question is the driving force behind the creation of Everyday Explanations. While on a bus ride home after middle school one day, my friend Kyle and I began debating each other as to whether or not this was possible.

I can't remember the conclusion we came to at the time, but I do remember learning our answer during a High School Math Class. Here's how we came to the conclusion that time traveling is impossible by simply moving faster:

Let's take a distance of 100 feet and create a chart for how long it takes to arrive based on speed of travel.

Looking at the chart we can see that as I move faster my time decreases, but at a rate proportional to my speed increase. For example, when I move at 20 ft/s it takes me 5 seconds to move 100 feet, while at 40 ft/s it will only take me 2.5 seconds. But when I move at 60 ft/s I will not arrive in 0 seconds, instead it takes me 1.67 seconds.

Notice that each column's values will multiply to a product of 100. This makes sense because we would multiply (ft/s)*s = ft, and the distance is 100 feet. So in order for time to be a negative number, we would need to have negative speed. This means that no matter how fast we

We can actually represent this truth graphically as well. Take a look at the graph of the charted points and you will notice that the time never actually reaches zero. Instead it just "flattens out" This means that no matter how fast I can move I will still always have a positive time and I will never be able to arrive before I leave.

The graph shows the concept of a "limit," which are critical to the study of Calculus. Limit means that the graph will continue to get closer to a point without ever actually reaching it. In this instance, the Limit for time as speed increases forever will be 0. Times will get smaller and smaller, but will never actually reach 0.

Using the equation from above, do your best to explain why that makes sense in the comments below.