Jade and her roommate jari commute to work each morning...

Jade and her roommate Jari commute to work each morning, traveling west on I-10. One morning Jade left for work at 6:40 A.M., but Jari left 20 minutes later. Both drove at a constant speed. The following graphs show the distance (in miles) each of them has traveled on I-10 at time t (in minutes), where t = 0 is 7:00 A.M. Distance traveled (mi) Time Since 7:00 A.M. (min) (a) Use the graph to decide which of them is traveling faster. Jade Jari (b) Find the speed (in mi/h) at which each of them is driving. Jari mi/h Jade mi/h (c) Find linear functions f and g that model the distances that Jade and Jari travel as functions of t (in minutes). Jari d(t) = Jade d(t) =

Transcript

00:01 So in this problem, what you're given is a graph to represent the distance that jade and jerry are from leaving their house.

00:07 So notice in the word problem, it says that jade left for work at 6 .50 a .m.

00:11 And jerry left 10 minutes later, which is why, remember, the graph is according to time since 7 a .m.

00:18 So in part a, we want to use the graph to decide which of them is traveling faster.

00:23 Well, notice, over this six -minute period of time, jerry went seven miles, and jade only went to.

00:30 10 miles, or sorry, six miles.

00:32 Because remember, she was already 10 miles away.

00:34 So therefore, that tells us that jerry would have been driving faster.

00:39 And let me put in the ordered pair here.

00:40 This is 6 and 16.

00:42 So like i said, j was already 10 miles away and is now only 16 miles away.

00:47 So that would be a difference of 6.

00:49 Okay.

00:50 Now for part b, we want to find their speed at which each of them is driving.

00:55 Well, remember, the speed is going to be the rate of change.

00:58 And the five rate of change, which we just have to find the slope.

01:01 So we're just going to find the slope of each of these lines.

01:03 To do this, we can use rise over run.

01:05 So i'm going to start with jerry.

01:08 So we're starting at the origin.

01:10 So to get to the order of pair 6, 7, we'd have to go up 7 units and over 6 units.

01:14 So it would be 7 over 6.

01:16 But notice your units.

01:17 This would be miles per minute.

01:20 Because remember, the denominator is in terms of minutes, not hours.

01:23 So to convert this to miles per hour, keep in mind, there's 60 minutes in an hour.

01:27 So we would need to multiply by 60 minutes over one hour, because then our units for minutes will cancel...

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