About this video
Justin runs 17 kilometers in 2 hours at a constant rate. The instructor writes d = k × h, uses the given values to solve for k = 17/2 = 8.5 kilometers per hour, and writes the final equation d = 8.5h.
You'll be able to
- write d = kh for a constant rate situation.
- find the constant k by dividing the distance by the time.
- include units, like kilometers per hour, with the constant of proportionality.
Key words
- constant rate
- Going the same distance every hour (or every unit of time).
- proportionality constant
- The number k that you multiply time by to get distance.
- kilometers per hour
- How many kilometers are covered in one hour.
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.
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