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# Writing proportional equations

## Video transcript

- [Instructor] We're told that Justin runs at a constant rate, traveling
17 kilometers in two hours. Write an equation that
shows the relationship between the distance he
runs, d, in kilometers and the time he spends
running, h, in hours. So, pause this video and see
if you can work through that on your own before we do it together. All right, now there's several ways to approach this question. One way is to say, look, he's
running at a constant rate, so his distance is going to
be equal to some constant, let's just call that lowercase k, times the amount of
time he spends running, and the way that we can
figure out what k is is by using the information
that they gave us. They tell us right over here that when our distance is 17 kilometers, so when our distance is 17 kilometers, that's a situation where he
has been running for two hours. So, that is going to be
equal to k times two hours. So, what is k going to be? Pause the video again and
see if you can figure it out, if you didn't figure it out the first time I asked you to pause the video. All right, well there's a
bunch of ways to solve for k, but one way is to say, let's just divide both sides by two hours. So, if you divide both sides by two hours, you are going to get that k is going to be equal 17 over
two kilometers per hour, which is, 17 over two is 8.5, 8.5 kilometers per hour. And so, if we go back to
the original question, which asks us to write an equation that shows the relationship
between d and h, we can say that d is equal to, we now know our proportionality constant, it is 8.5 times h. 8.5 times h, and we're done. If we wanted to write their units, we could write d is equal to 8.5 kilometers per hour times h, which is given in hours.