Race Times

We're getting ready for the two hundred fifty kilometer race, and the random generator gave us a slope of two point five two and a y intercept of fifty.

So how can we use this information to find out how long our racer will take to reach the finish line of the two hundred fifty kilometer race?

Let's start by writing an equation in the form of y equals m x plus b. Y equals two point five two x plus fifty.

Now before we jump straight into solving, it's really helpful to use a graph to get a quick estimate first.

To graph a line, we need ordered pairs. I'll plug in values for x and calculate y.

Like always, it's a great idea to start with zero. When x equals zero, y equals fifty.

Let's try a couple other nice round numbers. When x equals twenty, y equals one hundred point four. When x is fifty, y equals one hundred seventy six.

Now we can plot these ordered pairs on the graph. It's okay if you can't be perfectly precise. The graph is just helping us estimate.

Once the points are down, let's draw a line of best fit.

The finish line of the race is at two hundred fifty. By looking at where the line hits two hundred fifty, it looks like the racer will get there at around seventy seven minutes.

That's our estimate.

Now let's get more precise using the equation.

We want to know how long it takes the racer to reach two hundred fifty kilometers. So I will plug in two hundred fifty for y.

Two hundred fifty equals two point five two x plus fifty.

Remember the racer starts with a fifty kilometer head start, so it's not actually traveling the full two hundred fifty kilometers. It's really only traveling a distance of two hundred kilometers.

I can subtract that head start. If I subtract that head start of fifty from both sides, I'm really asking how long will it take the racer to travel two hundred kilometers at a rate of two point five two kilometers per minute.

If two hundred is equal to two point five two times x, that also means that two hundred divided by two point five two equals x.

Two hundred divided by two point five two equals about seventy nine point three seven minutes.

That's the exact time it will take the racer to reach the finish line.

Let's check. Is that close to our estimate of seventy seven minutes?

Yes. It makes sense.

If it weren't close, that would be a sign that I made a mistake somewhere and I need to investigate.

That's how we can use graphs and equations together to figure out how long a racer will take to reach the finish line.