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## Compare and interpret constants of proportionality

## Video transcript

- We're told that cars A, B, and C are traveling at constant speeds and they say select the car
that travels the fastest and 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. Alright, 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 is equal to D. Alright, now, let's see if
we can translate this somehow into kilometers per hour. So, 55h is equal to D or we could say D is equal to 55H and here I'm doing, this is this scenario right over here, not scenario A. And so, another way
to think about it is distance divided by time, so if we divide both sides by hours, we would have distance divided by time, and so 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 it tells 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 three is what? That is going to be, let's do it in our head, I think it's 45 but let me just verify that, three goes into 135, three goes into 13 four times, four times three is 12. You subtract, you get, yep, three goes into 15 five times, five times three is 15. Subtract zero. So, this is equal to 45 kilometers per hour. So, car A is 50 kilometers per hour, car B is 55 kilometers per hour, car C is 45 kilometers per hour, so car B is the fastest.