Video: Deciding Whether Two Quantities Are in a Proportional Relationship or Not

An elevator ascends or goes up at rate of 750 feet per minute. Is the height to which the elevator ascends proportional to the number of minutes it takes to get there?

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Video Transcript

An elevator ascends or goes up at rate of 750 feet per minute. Is the height to which the elevator ascends proportional to the number of minutes it takes to get there?

Let’s start this question by noting that we’re given a rate of 750 feet per minute. We could note this as a fraction of 750 over one. So, let’s take a look at the height that the elevator will ascend for a few different values of the number of minutes. In one minute, we know that the elevator will ascend 750 feet. In two minutes, we’d have two lots of 750 feet, so that’s 1500 feet. In three minutes, we’d have three lots of 750 feet, which is 2250 feet.

In this question, we’re asked if height is proportional to the number of minutes, so let’s recall what it means to be proportional. We can say that two quantities 𝐴 and 𝐵 are in proportion when from one situation to another both quantities have been multiplied or divided by the same number. So, in our first situation, we had 750 over one. That’s 750 feet in one minute. At two minutes, we had the fraction 1500 over two. That’s 1500 feet in two minutes. And at three minutes, we had 2250 feet over three minutes.

We notice that we could get from our first fraction to our second fraction by multiplying the numerator and denominator by two. We can go from our one minute to our three minutes by multiplying our first fraction, 750 over one, by three. Therefore, we can say that our fractions are equal. And therefore, we must have a proportional relationship. So, our answer to the question, is the height proportional to the number of minutes, is yes.

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