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.
