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Solve each problem by using a system of three equations inthree unknowns.

Three-day drive. In three days, Carter drove 2196 miles in 36 hours behind the wheel. The first day he averaged 64 \mathrm{mph}, the second day 62 \mathrm{mph}, and the third day 58 \mathrm{mph}

If he drove 4 more hours on the third day than on the first day, then how many hours did he drive each day?

First $10 \mathrm{hr}$, second $12 \mathrm{hr}$, third $14 \mathrm{hr}$

Algebra

Algebra 2

Chapter 4

Systems of Linear Equations

Section 3

Systems of Linear Equations in Three Variables

Polynomials

Systems of Equations and Inequalities

Introduction to Algebra

Graph Linear Functions

Write Linear Equations

Linear Equations and Functions

Matrices and Determinants

Johns Hopkins University

University of Washington

University of Michigan - Ann Arbor

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So you're getting the worst problem. Um, about a driving trip, You know that it's a three day driving trip. Um, so and it's asking about the how many hours did call you drive each day. So I'm gonna let you equal hours ribbon on the first day. Okay, um and then we know that the hours driven on the third day. So, um, our third day people's t plus four. Because they tell us that when we know that the total number of hours driven is 36. So we know ours. Driven on the second day equals 36 minus teeth, minus t plus four. Just gonna equal 32 minus two t. All right, so now we've have our initial variables, and now we have two. We've talked about time. We're gonna talk about distance. You know that the distance on the first day, thanks to call that you want close the distance driven on the second day, plus the distance driven on Thursday because the total, which is 2196. Um, yeah, 2196 miles. We also know the speed that he drives on each day. Right? And we know that speed times time is distant, so we know that 64 kinds t that's do one plus 62 times 30 to minus two t plus six b I'm t plus four equals 2196. All right, so now I can actually go through and self a. T your the 64 key. Plus, now we have a 62 times 32 19 be four minus one 24 teeth plus 50 80 plus 58 times for just 232 goes 2196. Now clean this up. We have a 64 t minus 1 24 t plus 50 80. That's a negative two t equals and then we have a 2196 minus 19 beauty four minus 2 30 to his negative clinic. The T equals tap so we know that he drives 10 hours on the first day, 14 hours on the third day, 10 hours on the first day, 14 hours on Thursday and then 64 minus tan minus 14. This Ford 40 hours the second that we've solved. How many authority drives

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