Unit Rate

This motor racer is traveling at a constant rate of zero point one six meters every three seconds. If we know how far it travels in three seconds, how can we figure out how far it will travel in, let's say, ten seconds?

Knowing the three second rate is helpful, but not all times are multiples of three. We need a more flexible tool. Something that works for any amount of time.

In the last lesson, we split up six and nine second time trials into three second chunks. This time, let's split up that three second time trial into even smaller chunks, and find out how far it travels in each one second part.

This bar shows three seconds of time, and the total distance point one six meters stretches across the whole thing. I am going to divide this bar into three smaller equal parts.

Point one six divided by three. When I divide, I'm going to get a number that goes all the way to the thousandths place. That precision matters, because our racer's distances are rather small. Just a few tenths of a meter. So even tiny differences can make a big impact.

Point zero five three. That tells us the racer travels about point zero five three meters every one second. That's just over five centimeters per second. This is called the unit rate.

It's useful because once we know the racer's per second rate, we can figure out how far it goes in any amount of time.

Now, we can use the unit rate to figure out distances for any time. Using a calculator, I can quickly record the distances in a table that will allow me to reference different amounts of time very quickly.

In ten seconds, the racer will travel point five three meters. Let's extend the table all the way to twenty seconds.

Now instead of running new trials for every time, all the predictions are right in front of us.

That's why scientists, engineers, and mathematicians always use unit rates. They turn one piece of information into a whole model.