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# Comparing proportionality constants

CCSS.Math:

## 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 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 55 H is equal to D all right now let's see if we can translate this somehow into kilometers per hour so 55 H is equal to D or we could say D is equal to 55 H 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 they tell us DS and kilometers H is in hours so the units here are going to be kilometres per hour so car B is going 55 km/h 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 in three hours and so we can get the rate per hour so 135 divided by three is what that is going to be lets you do it in our head it's I think it's 45 but let me just verify that 3 goes into 135 3 goes into 13 4 times 4 times 3 is 12 you subtract you get yep 3 goes into 15 five times 5 times 3 15 subtract 0 so this is equal to 45 km/h so kharece 50 km/h car B is 55 km/h car C is 45 km/h so car B is the fastest