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Ch 02: Motion Along a Straight Line
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All textbooksYoung & Freedman Calc 14th EditionCh 02: Motion Along a Straight LineProblem 2

Chapter 2, Problem 2

You normally drive on the freeway between San Diego and Los Angeles at an average speed of 105 km/h (65 mi/h), and the trip takes 1 h and 50 min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average speed of only 70 km/h(43 mi/h). How much longer does the trip take?

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Welcome back everybody. We are taking a round trip walk between a park and a rec center. So I'm gonna go ahead and label park sp and the rec center as our and like I said, it is round trip meaning that we are going to and from now I'm going to let d be a variable that represents the entire distance we cover during that round trip or our round trip Distance. Now, every single time we take this trip, we are walking at an average speed of 5. km/h And walking at that speed to cover that entire distance, it takes us a time of 1.5 hours. Now, one day we decide to pick up the pace and we are going to jog that distance and we are going to jog at a speed of 10 km/h on average. And we are asked to figure out what the time for that trip now is. Now. In order to figure this out, we're gonna have to set up a system of equations and solve for variables. And the easiest thing that is pointed out to me is that we can solve for D. Now, D. E is our round trip distance. And in order to find D we just multiply a velocity times time, we know that according to our kid a Matic equations. Now let's go ahead and plug in our initial known velocities in our initial known time, This is going to be equal to 5. kilometers per hour Times 1.5 hours. This is going to be equal to 8. kilometers. Now that we know D. We can solve for T. Two by multiplying T two by V two and setting it equal to D. So let's go ahead and do that. So D equal to V two, T two, And this is really 8.1 km equals 10 kilometers per hour times T two. Now, in order to solve for T two, let's go ahead and isolate that variable by dividing by 10 on both sides, so T two equals 8.1 divided by 10, Which equals 0. hours. This is going to be our final answer, which corresponds to answer choice. D Thank you so much for watching. Hope this video helped, and we will see you all in the next one.
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