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## 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?(12 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.(11 votes)

- how do you do 2 + 2(12 votes)
- + means the second number more than the first number(1 vote)

- "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 :)(1 vote)

- nothing makes sense :/(4 votes)
- Isn't car B going 1 kilometer per 55 hours?(4 votes)
- how do you know if you have to just divide h(3 votes)
- because you have to get the number by itself(so 55 in our case), so you divide h to isolate the 55(3 votes)

- this is confusing me(4 votes)
- you are right to not get car b. they give you the equation

55h = d

but the problem is that a variable like "h" or "d" can only be an amount like "10" or "42" or it can be an amount with units like "10 bananas" or "42 cats".

you CAN say

5 = 5

but you can't say

5 apples = 5 oranges

because the units are different.

you can NOT say

km = hour (different unit problem)

so you can't change 50km/hour into an equation like

50 = km/hour

This is a mistake. The exercises in the proportionality section have many mistakes because they are misusing equations. I sent a message to khanacademy with the hope that they will address this issue. To get through this section I suggest that you imagine "=" to be like a ":" instead(4 votes) - This doesn't make sense with the work sheet(3 votes)
- i get it so the distance of the car in blank hour so you need to take the distance multiply by the hours and you get the answer. am i right(3 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.