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

In three days, Katy traveled 146 miles down the Mississippi River in her kayak with 30 hours of paddling. The first day she averaged 6{mph}, the second day 5{mph}, and the third day 4 {mph}. If her distance on the third day was equal to her distance on the first day, then for how many hours did she paddle each day?

8hours, 10hours, 12hours

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 North Carolina at Chapel Hill

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University of Michigan - Ann Arbor

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all right. So given a word problem here and I'm first thing that x y z before the hours she paddled beach So axes the arch a panel on the first day. Why secondary disease? I'm third. So now we need three equations to solve. This one is easy. We know the hour she paddled on the first day equal the hour and she paddled from on the sorry The distance on the third day was equal to the distance On our first day we know that distance It's Eve but we know that distance on the first day. Just six acts equals four Z that she's going six miles an hour on the first day, four miles hour on the third day. Then you know that X plus why Z equals 30. And finally, we know that six acts plus five y plus four z equals 146. Now you re equations that we can use to solve here. If we solved her acts, we're gonna get X equals 4/6 times Z. It's parentheses for us. So now we can we have acts in terms of Z now we just need why in terms of C. Um, and we could get this using the second equation we have. Why be close? 30 minus X minus Z. And we know that access for six busy. So this is gonna before about six Z. Um, if you add, this is the same thing at six. Over six. Is he was actually just gonna be can over six t. So now we have accent wife Suzy. We can plug it into the third equation solvers E. So we have six times acts, which is six times for over six z plus five fans thirties, minus 10/6 Z four z people 1 46 calculators. Uh, you know, six times 4 60 is 24/6, which is just four. So four z. Let's make sense because we know that six x equals 40. We didn't even really have to substitute in for X here. We know that six X equals four z. We complain and four Z right there. Um, so we have 40 plus one minus 300 over six. Um, because that's five times 10. Sorry. 50. Because if you know about this five through, it's gonna be 50. Um, over six Z so much. 50/6 z plus for the equals 1 46 Um, you can subtract this 1 60 to be negative. Before now you're gonna have eat Z minus 50/6. So if you take eat and subtract 50 about it by six, you're gonna be left with negative 1/3. So negative warm Thurdsay close. Negative. Four. Um, that means he is gonna equal 12 if you take negative 1/3 and multiply that by 12 you're gonna get negative four. So now we have Z just the our ship out on the third day. You know that Z equals acts. So X is also sorry if you know that um, four is equal. Six acts so X equals 4/6 times E, which is going to give us eat. So executing people eat and then why is gonna equal 30 minus 10/6 times Z, which is 12? That's gonna be so you know, she pal. Eight hours on the first day when I was on the second day in 12 hours

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