Question

Sarah wants to buy the car that has a better mileage rating. Cars of Company A travel 20 miles per gallon and cars of Company B travel 14 km per liter.

[1 mile = 1.6 km; 1 gallon = 3.79 liters]

Part A: Which company's car should Sarah buy? Justify your answer by comparing the mileages after converting to the same units. (5 points)

Part B: If 10 gallons of gas is filled in the car which gives better mileage, and you went on a drive and checked on the gas used every 30 miles, describe appropriate scales on the x-axis and y-axis to graph the rate at which the car uses gas. (5 points)

Answer 1

Hi @Lena772,

How far did you get with this one?

Answer 2

Hey. I'm wondering if I should convert km per liter or miles per galon or viceversa

Answer 3

There are a couple reasons to convert everything to gallons:

1. In the US, most cars and gas stations use the miles per gallon rate.
2. The second question speaks in terms of gallons

So it definitely makes sense to use gallons.

Answer 4

Do you agree?

Answer 5

Yes

Answer 6

14/1.6 = 8.75 miles

Answer 7

By the way, did you convert km to miles or liters to gallons?

Answer 8

Km to miles

Answer 9

The reason why I asked is because we were given a rate 14 km/L
We have to convert 14km/L to mi/Gal

Answer 10

Do you get what I mean here?

Answer 11

yes

Answer 12

I mean if we were only given km, then we could directly convert that to miles, but that's not what we were given.

Answer 13

right

Answer 14

In order to convert 14 km/L to mi/Gal, we have to do something like this:

\[14 \frac{\text{km}}{\text{L}} \times 3.79 \frac{\text{L}}{\text{Gal}} \times\frac{1}{1.6}\frac{\text{m}}{\text{km}}\]

Answer 15

Then cancel the appropriate units and multiply the numbers to end up with mi/Gal

Answer 16

\[14 \frac{\cancel{\text{km}}}{\cancel{\text{L}}} \times 3.79 \frac{\cancel{\text{L}}}{\text{Gal}} \times\frac{1}{1.6}\frac{\text{m}}{\cancel{\text{km}}}\]

Answer 17

\[\frac{(14)(3.79)}{1.6} \frac{\text{mi}}{\text{Gal}}\]

Answer 18

You may have never seen this kind of conversion before but it is called unit-rate conversion.

Answer 19

Basically, after conversion you end up with approximately 33 mi/Gal

Answer 20

like molar ratio kind of?

Answer 21

Whatever helps you understand it. I'm not a chemistry major so not familiar with the term "molar"

Answer 22

But I believe now we have enough information to answer the first question.

Answer 23

yeA

Answer 24

So which car should Sarah buy and why?

Answer 25

Car from company B because it has a better gas mileage.

Answer 26

Yes, company car B is the obvious choice. Now, how will you answer question B?

Answer 27

I suck at graphs I have NO idea

Answer 28

At the very least, we should be able to figure out units to use for the x and y axes. What units should we use per axis?

Answer 29

gallons on x?

Answer 30

Remember, the x-axis represents the independent variable. The y-axis represents the dependent variable.

Answer 31

Also remember that in general the rate will be y/x

Answer 32

the unit rate

Answer 33

but both of the variables are changing

Answer 34

so how is one independent

Answer 35

Think of it this way, we need the gas to be able to go anywhere. Without the gallons of gas, no travel is possible.

Answer 36

Also, we can fill the car with however many gallons we want without going anywhere. Or we can remove the gas from the car without going anywhere.

Answer 37

However, we can't travel any miles without the gallons of gas.

Answer 38

So that should be enough for you to understand why gallons is independent and why miles is dependent.

Answer 39

so like i said gallons on x

Answer 40

Furthermore, the rate is represented by

\[\frac{y}{x} = \frac{\text{mi}}{\text{gal}}\]

Answer 41

So by default, the fraction mi/gal let's us know which axis to put the units.

Answer 42

Right

Answer 43

what about scales

Answer 44

So far this is what we know graphically: