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Problem 16 Medium Difficulty

Jason leaves Detroit at 2: 00 PM and drives at a constant speed west along $\mathrm{I}-94 .$ He passes Ann Arbor, $40 \mathrm{mi}$ from Detroit, at 2: 50 PM.
(a) Express the distance traveled in terms of the time elapsed.
(b) Draw the graph of the equation in part (a).
(c) What is the slope of this line? What does it represent?

Answer

a. $48 \mathrm{mph}$
b. See the graph in the full solution.
c. The slope is $\frac{4}{5}$

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Video Transcript

So we know that Jason leaves Detroit At two PM and drives a constant speed um passing in a harbor which is 40 miles from Detroit at 2 50. So that means that it took 40 miles or in 40 miles that took 15 minutes. But we know that 50 minutes needs to be written in terms of hours, so we'll have 50/60. That means that they were going 48 mph. And then we want to draw a graph of the equation in part A. So we see if they're going 48 miles an hour, we can just write Y equals 48 X. And that will define their distance from Detroit. And then we see that the slope of the line is going to be 48 and that's going to represent the velocity or the speed because you know, the velocity is going to be, the derivative will eventually the velocity is the derivative of this position function.

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