Modeling distance over time

0:00- [Instructor] At its current constant speed, a train travels 50 kilometers in 10 minutes and they'll let t equal time in minutes and d equal distance in kilometers. Part one, well, actually I encourage you to pause the video and try to do all of these parts and then let's do it together.

0:15So part one says write a formula for distance in terms of time. So generally speaking, we can think of distance is equal to rate times time and we can figure out the rate because they tell us the speed, at its current constant speed, it can travel 50 kilometers every 10 minutes.

0:33So one way to think about it is the rate is going to be equal to 50 kilometers every 10 minutes. And that's the same thing as if we just say 50 divided by 10, that's five kilometers per minute. So that's our rate. And so if we want the distance in terms of time, it's just going to be five kilometers per minute times our time.

1:02So 5t. Next, write a formula for time in terms of distance. There's a couple of ways we could approach this. The way I would do it is just start with the equation we wrote in part one and solve for t. So if d is equal to 5t, if we divide both sides by five, and why am I doing that?

1:25Well, then if I have 5t and I divide it by five, I'm just going to be left with a t on the right. But if I do it to the right side, I have to do it to the left side as well. So I'm going to get t is equal to d over five. T is equal to d over five. And all I did is I took this top one and I divided both sides by five.

1:44If two things are equal to each other, as long as I do the same thing to both, then the next statement I get will be true. Part three, complete the table to show the relationship. So the first one, this first row here, they give us distance but not time. So it'd be useful to use this second equation or formula, whatever we wanna call it, because this solves for time when we're given the distance.

2:09So we know that time is equal to distance divided by five. Our distance is 10. So if we divide that by five, we are going to get two minutes. And all I did is apply this. I just said t in this situation is going to be equal to our distance, 10 divided by five.

2:26All right, the next one, we're given time, we want distance. Well, here I would use this first equation or this first formula where we know that distance is equal to five times the time. In this case, five times four, it's going to be equal to 20 kilometers. And then last but not least, they give us the distance again, want us to figure out the time.

2:47Well, we already know how to solve for time in terms of distance. T is equal to distance, 35, divided by five. I'm just applying this, which is equal to seven. Seven minutes. So now they want us to plot these three points and draw a straight line through them.

3:07So actually I'm going to use some colors here. That's always fun. So this first one, time, two minutes, distance, 10 kilometers. Time, two minutes, distance, 10 kilometers. That's that point right over there. This next one, time is four minutes, distance is 20 kilometers.

3:25Four minutes, 20 kilometers, that point right over there. And then last but not least, we have time at seven and distance at 35. Time, seven minutes, distance at 35. And now I just need to connect those points. Okay, so I can make one end to go through one of these points right like that.

3:51And you could use a ruler if you wanted or maybe even the side of a notebook. It might look something like that and I just have to connect the points. There we have it. I have done all of what people ask and it's always good to do a reality check to just make sure it makes sense.

4:08At zero time, we've gone zero distance. And then every minute, notice, I've gone five kilometers. Every minute, if you take the number of minutes and you multiply by five, you figure out how far you've gone. Every extra minute I go five more kilometers. Every extra minute I go five more kilometers.

4:26And it's a constant speed so it makes sense that that trend just keeps going throughout this line.