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## Pre-algebra

### Course: Pre-algebra > Unit 7

Lesson 9: Analyzing relationships between variables# Analyzing relationships between variables

Rava is studying an electric car. She finds out that the more she charges the car, the further it can go. The relationship is simple and direct: more charging time equals more distance. This helps her predict the car's range based on how long it's been charged. Created by Sal Khan.

## Want to join the conversation?

- i dont get it...(5 votes)
- I don't get why Sal doesn't also say you can divide k by t to get the number of K per t (when doing part 1).

If you're gaining 180km per 15 minutes of charging time, isn't it easier to just divide? From there you know Per minute (t) you are gaining 12km of range(k).(2 votes) - you can also do the following if you dont want to do it how sal did it. take how many times the number is increasing which is 180, now the charging time is increasing by 15 minutes so now you need to find how many km it can go in 10 minutes.so from 15 to 10 so its a 5 minute difference so divide 180 by 3 because 15 to 30 its increasing by 180 km so you get 60 so subtract 180 by 60 and you will get 120 and 10 times 12 is 120. so there you go thats how you can get the same answer as sal doing it a different way hope that helped(2 votes)
- Why is there only 3 comments? (Excluding me)(2 votes)

## Video transcript

- [Narrator] We're told Rava
is researching an electric car. She finds this graph,
which shows how much range, measured in kilometers, the car gains based on charging time. All right, and they say, first, fill in the missing
values in the table below. And if you are so
inspired, pause this video, and see if you can have
a go at that as well. All right, well they give us a few points, and I'm assuming these
are points on a line. And we can see when the
charging time is 15 minutes, the range is 180. So we could see when the
charging time is 15 minutes, the range is 180. We can see when the
charging time is 30 minutes, the range is 360 kilometers,
so I could write that there. And then we see when the
charging time is 45 minutes, the range is 540 kilometers. So that's all nice. But then they give us a
few other points here. They say what happens when
we are at T equals 10, or T equals one, which
aren't easy to pick out here? But this is where it might be useful, if we assume that this is a line, what is the relationship between these? So let's see, to go from 15 to 180, it looks like you're multiplying by 12. To go from 30 to 360, it looks
like we're multiplying by 12. To go from 45 to 540, it looks like we are multiplying by 12. So assuming K is just
going to be 12 times T, we know that when T equals one, K is 12, and when T equals 10, 10 times 12 is 120. All right, now the second part,
they say write an equation Rava can use to find out
how much charging time, T, it takes to gain any number
of kilometers in range, K. All right, well we already
established a relationship. We said that K is equal
to 12 times whatever T is. That's what we just established
in this table up here, but that's not what they want. They wanna find out how
much charging time, T, it takes to gain any number
of kilometers in range, K. So what we need to do here is solve for T. So let's divide both sides by 12 to just have a T by itself
on the right-hand side. And we are going to be left
with T is equal to K over 12. T is equal to K over 12 and notice, you could put any number of
kilometers of range in here and you're essentially just
going to divide it by 12, and that will give you
how much charging time. And I guess this would assume
an infinitely large battery, which we know doesn't exist. But for the sake of this
problem, here we have it. Here is the equation Rava can use.