Comparing proportionality constants

We're told that cars A, B, and C are traveling at constant speeds, and they say select the car that travels the fastest. We have these three scenarios here, so I encourage you to pause this video and try to figure out which of these three cars is traveling the fastest: Car A, Car B, or Car C.

All right, now let's work through this together.

So Car A, they clearly just give its speed: it's 50 kilometers per hour. Now, let's see. Car B travels the distance of D kilometers in H hours. Based on the equation 55H = D.

All right, now let's see if we can translate this somehow into kilometers per hour. So 55H = D, or we could say D = 55H. Here, I'm doing this in this scenario right over here, not scenario A.

Another way to think about it is distance divided by time. If we divide both sides by hours, we would have distance divided by time. If we have D over H, then we would just be left with 55 on the right-hand side. All I did is I divided both sides by H.

Now this is distance divided by time, so the units here are going to be—we're assuming, and they tell us D is in kilometers, H is in hours—so the units here are going to be kilometers per hour.

So Car B is going 55 kilometers per hour, while Car A is only going 50 kilometers per hour. So, so far, Car B is the fastest.

Now, Car C travels 135 kilometers in three hours. Well, let's just get the hourly rate, or I guess you could say the unit rate.

So 135 kilometers in three hours, and so we can get the rate per hour. So 135 divided by 3 is what that is going to be. As you can do in our head, I think it's 45, but let me just verify that.

3 goes into 135; 3 goes into 13 four times. 4 times 3 is 12. You subtract, you get—yep, 3 goes into 15 five times. 5 times 3 is 15; subtract 0.

So this is equal to 45 kilometers per hour.

So Car A is 50 kilometers per hour, Car B is 55 kilometers per hour, and Car C is 45 kilometers per hour. So Car B is the fastest.