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### Course: 7th grade (Illustrative Mathematics) > Unit 2

Lesson 7: Lesson 9: Solving problems about proportional relationships# Comparing proportionality constants

Sal compares constants of proportionality in various forms, such as graphs, equations, contexts, diagrams, and tables.

## Want to join the conversation?

- What was the point of switching 55h=d to d=55h? Isn't it the same thing?(21 votes)
- In terms of a proportionality constant, d=55h is the correct form of y=kx as the basis of a direct variation with d as the dependent and h as the independent variable. If you switched variables, you would have h = 1/55 d where h is now the dependent and d is the independent with a k= 1/55. They are the same, but the second is the correct form.(30 votes)

- I remember 2 years ago, the comments section wasn't so spammed and trash as it is now. People asked questions and the given answers brought me more questions, mostly because I didn't understand a thing they said.(23 votes)
- I think the biggest reason is that most people are not interested in writing comments that improve Khan Academy. the best thing we can do is write the kinds of comments we want and stay within the unit/page/video we are on.(7 votes)

- I'm a bit confused with B...

If`55h=d`

is car B's speed, and h is hours, and d is kilometers, wouldn't this mean that it takes 55 hours (h) to drive 1 kilometer (d)? Or am I misunderstanding this somehow?(8 votes)- In the video, Sal states that another way to think about the equation is distance divided by time. This can be written into the fraction d/h, and can be seen in Scenario A, which is Car A. It is shown that Car A travels at 50 km/h. In Scenario B, d is shown to be the variable for kilometers, meaning the fraction d/h can also be thought of as km/h, or kilometers/hours.

The reason why it might be confusing to look at that equation is because it could appear to be 55 hours = 1 kilometer. However, these variables do not have values; variables are meant to represent the numbers that the value of are unknown. In other words, it might seem that the equation states that 55 hours = 1 kilometer, it is really just stating that 55 is the constant of proportionality between h and d. The variables in the equation could be any number, and they represent unknown values. You could also think about it like the variables are placeholders to represent numbers that we do not know. Even though it might look like 55h=d is equivalent to 55 hours = 1 kilometer, these variables could be any number.

Simply put, these variables could be 1,583,520,6058, or -5,019. The variables are just there to represent these numbers. This is why algebraic problems with variables have a goal of finding the value of the variables based on the known numbers around them.

In this case, 55 is only the constant of proportionality between h and d.

Hope this helps! Sorry if I rambled a bit too much!(24 votes)

- how do you do 2 + 2(13 votes)
- + means the second number more than the first number(3 votes)

- nothing makes sense :/(11 votes)
- nothing ever makes sense(2 votes)

- Hello from 2024(9 votes)
- I watched this five times and it won't mark it off. What do I do.(6 votes)
- watch it without skipping parts(2 votes)

- "Car B travels a distance of d kilometers in h hours, based on the equation 55h = d"

so if d is a variable representing the amount of distance travelled &&

if h is a variable representing the amount of hours travelled then

the equation is a relationship of these amounts and is understood as:

for every d traveled you spend 55 times an amount of h time.

there isn't enough information to say the speed because h isn't a unit and d isn't a unit but they are amounts.

you can't have hours == to time since they are different units.

you can't say 5 hours equals 10 meters.

you can say that amounts are equal:

2 x5 = 10(5 votes)- Actually, the equation is interpreted as :

You travel for h hours, the distance you cover will be 55 times the no.of hours you traveled for.

Both d and h are quantities : d represents the distance traveled, while h represents the number of hours you traveled for, i.e., time.

Units are also mentioned : d is measured in kilometers, h is measured in hours. So, you have sufficient information to calculate the speed.

Hours is not equal to time, but it is a unit of measuring time.

Hope this helps :)(3 votes)

- 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.(5 votes)
- Yes

I will do so I divide 1 by 2 = 0.5(5 votes)

## 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.