solve-each-problem-by-using-a-system-of-three-equations-in-three-unknowns-three-day-drive-in-three-d

Question

Solve each problem by using a system of three equations in
three 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?

Jake Zanazzi · Accepted Answer

So you&#x27;re getting the worst problem. Um, about a driving trip, You know that it&#x27;s a three day driving trip. Um, so and it&#x27;s asking about the how many hours did call you drive each day. So I&#x27;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&#x27;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&#x27;ve have our initial variables, and now we have two. We&#x27;ve talked about time. We&#x27;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&#x27;s do one plus 62 times 30 to minus two t plus six b I&#x27;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&#x27;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&#x27;ve solved. How many authority drives

Jake Zanazzi · Answer

all right. So given a word problem here and I&#x27;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&#x27;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&#x27;s Eve but we know that distance on the first day. Just six acts equals four Z that she&#x27;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&#x27;re gonna get X equals 4/6 times Z. It&#x27;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&#x27;s make sense because we know that six x equals 40. We didn&#x27;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&#x27;s five times 10. Sorry. 50. Because if you know about this five through, it&#x27;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&#x27;re gonna have eat Z minus 50/6. So if you take eat and subtract 50 about it by six, you&#x27;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&#x27;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&#x27;s gonna be so you know, she pal. Eight hours on the first day when I was on the second day in 12 hours

Jessica Hill · Answer

in this problem were asked to show a complete solution, given the fact that we have of person A averaging 50 MPH and person B average is 56 MPH, and we know that person a drove for two more hours than Person B. Um, and a total of 683 miles were covered by the two of them. So we want to know how many hours did person a drive? Well, let&#x27;s go ahead and start setting up an equation to help us figure this out. Okay, so first of all, I know that a total of 683 miles was covered. Yeah, so I need to figure out what led up to that. So I&#x27;m going to have person A&#x27;s, a mileage plus person B&#x27;s. That&#x27;s when equal my overall of 6 83 So let&#x27;s go ahead and start with person A. They averaged 50 MPH, so 58 MPH if I take the rates multiplied by the time that they drove, which we don&#x27;t know either of their times. But we do know a person a drove two more hours than person B. So let&#x27;s say a person B&#x27;s hours of driving I&#x27;m gonna represent by using an X. If I add two, that will be how many hours person a job I&#x27;m So I will give me my total mileage per person? A. So I need to add on the mileage for person B. I know that person Be, um, job at a rate of 56 MPH, and we&#x27;re using X to represent how much time they drove. So now I have an equation that I can solve. So let&#x27;s go ahead and start by distributing this 50 into our princes here. So 50 multiplied by X is 50 x plus 50 times positive, too. It gives me 100 plus r 56 X equals 683. Okay, so now I can combine like terms. Here I have two x variable terms on my left side. So 50 X plus 56 x equals 106 x plus. 100 equals 683. It&#x27;s now I&#x27;m going to go ahead and take my 100 and subtracted from both sides. That&#x27;s going to leave me with 106 x equals 583. And then my last step is going to be going to be to divide off my 106 from both sides to isolate that variable. So 583 divided by 106 is going to give me five 0.5, so I&#x27;m gonna end up with X equals 5.5. So that is the amount of time that person be drove. Remember, X equals Person B&#x27;s time, and our question is, how many hours did person a drive? So if person A drove for two more hours than Person B that I&#x27;m going to take my 5.5 plus two hours, that&#x27;s going to give me 7.5 or 7.5 hours, So I&#x27;m going to write that out 7.5 hours for person. A. That is our solution

Jessica Hill · Answer

in this problem were asked to show a complete solution for the following. So we have two people that added together drove a total of 734 miles. You know that one person averaged 54 MPH and the other averaged 58 MPH in drove for three more hours in that first person. We want to know how many hours did the first did the person drive that drove the extra three hours at 58 MPH. So we need to set up an equation, help us solve this problem. So first piece of information that we have is that they drove a total of 734 miles. So I&#x27;m going to put that down here. And I know that if I take miles for our most blood, by the time that they drove, that&#x27;s going to give me the total miles that that person drove. So let&#x27;s deal with the first person. So we know that the first person that we&#x27;re talking about one person average 54 MPH, so 50 or MPH, And if we multiply that by the time that they took to drive that That&#x27;ll give me my total hours for a person number one. So we&#x27;re just gonna represent that using 54 X and then if I add our second person who drove 58 MPH and we don&#x27;t know how far he drove, that&#x27;s what we&#x27;re trying to figure out. But we do know that they drove for an additional three hours in the first person. So we&#x27;re gonna represent that using X plus that extra three hours. And now we have an equation that we can solve. Once we sell for X, we can figure out how much this second person at 58 MPH, drove. So let&#x27;s go ahead and start, and we&#x27;re going to start by distributing are 58 into our prince easier. So that only knew 54 x plus 58 times X gives me 58 x, then 58 times three equals positive. 174 equals a total of 700 34. Okay, so now we can combine like terms. So first we&#x27;re gonna take 54 plus 58 x is me 112 x plus 1 74 equals 734. And now I can take my 174 in subtract from both sides. That will leave me with 100 12 x or my left in 734 minus 174. Yes, me 500 60. So my final steps isolate my variable of X, and I am going to do this by dividing off my coefficient of 112. That&#x27;s when you leave me with X on my left in 560 but it by 112 gives me five. So I know that this first person shown right here in our equation my 54 x 54 multiplied by our ex of five hours. So that first person drove for five hours that we want to know how many hours the person drove that drove the extra three hours at 58 MPH. Well, if we have that first person driving five hours in the second person drove the next trip three and that is going to give us a grand total five plus three hours, we are it hours. That&#x27;s our solution

Fatih Kilinc · Answer

em and rode a snowmobile a trade off 200 miles per hour and then skied cross country a tradeoff for mile stare off. So we have the man&#x27;s snowmobiling, snow moral at the rate off to end the m p. H. And, uh, this key is four AM p. These are the speeds for his two wiggles around the amputation for mph. And we know that, uh, he traveled for the eight miles in total and this to the tree tube six ours. But we don&#x27;t exactly know how long did he use normal. And how long did he use this key? Actually, that&#x27;s the question. So we&#x27;re gonna assign, except why again, where X is the time that he used on this normal, his phone&#x27;s normal. And why is the amount of time that he spent on this key So Okay, so that means says it takes six hours in total, explores why should pay six. And we know this Pedes off the snowmobile and ski there, too. And the M P h and four mph. We will be able to multiply that Randy by the time that&#x27;s too. And the X and the four by the Why they will give us the distance. He too, for the each type. So too, and the explosives for why should be cool, too. 48 year. So this is our system. Well sold. This one that&#x27;s this time use like algebra. Fordice. So since V X plus Y and try and expose for why the car vision must be saying so. How about making that the first cooperation? Same. We multiply it by four. So when we do that, the first equation for X plus for why is he cool tube to enter four. And the second equation is just saying we don&#x27;t touch it for expose for Why is it cool to 48? We can&#x27;t let the wise by just subtracting them so four X minus two And the eggs with the native 16 x is equal to 24 minus 48 is native. 24. We&#x27;ll just divide both sides by negative 16 years. Negative. 16 onboard sites that will give us tax to enter four or 16. That will be three over to that 1.5 so that it takes 1.5 hours to drive the snowmobile. So we&#x27;re gonna plug 1.5 into one of these equations to see the time that this span on ski. Okay, so let&#x27;s use the first equation. So we&#x27;re plugging 1.5 in tow. Axl 1.1 1.5 plus, Why physical to six? If it&#x27;s subtract 1.5 on both sites, it will do us. Why is it cool to 4.5? So X is 1.5 physical to 4.5 the time that he drive the snowmobile 1.5 hours and 4.5 hours for the skiing.

Julie Silva · Answer

So in this problem were ultimately being asked to figure out how long it took her to drive from Harrisburg to Pennsylvania. Well, we&#x27;re also gonna need to maybe figure out how long it&#x27;s gonna take from Allentown to Harrisburg. So I&#x27;m gonna let X represent the time from Allentown to Harrisburg. And why is the time to get from Harrisburg to Pittsburgh? Well, we&#x27;re told the total duration of district trip is six hours. Therefore, we know X plus y is equal to six. Now, the second piece of information we&#x27;re talking about is the distance. Well, the total distance of the trip is 288 miles. Well, remember the formula distance is equal to rate times time. So it was first talk about the Allentown, the Harrisburg trip. Well, we don&#x27;t know the total distance of that, but we know the speed was 42 miles per hour and the time we don&#x27;t know, but we&#x27;re calling it X. So 42 x represents the distance from Allentown to Harrisburg. Well, we can do something very similar from Harris Harrisburg to Pittsburgh. In this case, D would be 51 times. Why? Because her average speed was 51 miles per hour. So plus 51 y is equal to 288. And now with salt or sorry. Now we&#x27;ve set up two equations. Remember? All we really need to find is why. So I&#x27;m gonna solve this by using on the addition method. And I&#x27;m gonna try and get rid of my axes because then I could solve for why? So they do that. I need to multiply both sides of the equation by negative 42. So when I do that negative 42 x minus 42. Why in negative 42 times six is equal to 252. Now we can use the addition method because 42 x minus 42 X cancels. We have 51 y minus 42. Why? Which is nine? Why? And 288 minus 2 52 is 36. So now to solve for why we just divide both sides by nine. And we find that why is equal to four, which remember why I&#x27;ve represented our time from Harrisburg to Pittsburgh. So it would have taken four hours

Problem

Solve each problem by using a system of three equ…

Problem 45 Hard Difficulty

Answer

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

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Mark Dugopolski

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Lily A.

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Solving Absolute Value Inequalities

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

Algebra for College Students

Lily A.

Grace H.

Shubham P.

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Solving Absolute Value Inequalities

Rewrite Equations and Formulas - Example 2

Mark DugopolskiAlgebra for College Students

Lily A.

Grace H.

Shubham P.

Kristen K.

Mark Dugopolski

Algebra for College Students