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Question

Using Models Use the model given to answer the questions about the object or process being modeled.

The distance $d$ (in mi) driven by a car traveling at a speed of
$v$ miles per hour for $t$ hours is given by
$$d=v t$$
If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

Kyle Icban · Accepted Answer

So we&#x27;re giving this problem by New Marie and reading out. But together we have this problem. The distance D in miles driven by car, traveling at a speed of V 30 hours, is given by de Eagles. Bt. So if the car is driving at 70 miles per hour for three and 1/2 hours, how far has it traveled? Things that this problem is giving us First, we have a formula and values, which are the numbers right over here. And the formula course holds variables, and the first step is to sign each of these values to variable in the equation. So looking back at the first portion of the question, we have our variables. D the ante and let&#x27;s assign these variables with different colors. So that&#x27;s have d be red v be green and tea be blue, all right. And looking at our values, we consign each of them to the variables just by looking at the definitions. So since V is miles per hour, the speed we can assign the 70 miles per hour two are variable. And similarly, since t is for time and has given hours, you gonna sign three and 1/2 hours to t. So let&#x27;s just be right. This honors on the side. So we have me equals 70 miles per hour. I&#x27;m going to rewrite this real quick as 70 miles her nose. The division sign our because the word per is really just a division sign. Right? So, miles per power. Okay. And then doing the same for tea? No, no special. We&#x27;re here. We have three and 1/2 hours. All right. Now, playing in a rallies to our equation. We had d is equal to Vt or 70 miles per hour times time, three and 1/2 hours and do this way you&#x27;ll notice that the hours are gonna end up canceling out, do the community property. And what we&#x27;re left with is just miles on top, which makes sense because we&#x27;re looking for a distance. So using a calculator, we can multiply 70 and 3.5. And so what we&#x27;re gonna get is that D is equal to 245 miles necessary. Aunty

Ankit Gupta · Answer

Hello! Stand nowhere would understand its course in the distance D Brevin by a car travelling at a speed off we miles. For our part, B r is given by be acquired toe be be no guarded difference, 20 miles so obvious given them. But the B is given which is equal to 70 miles. What are and time be, which is given 3.5 power Now, how hard has it ever? So finding distance. So we interpret be given 70 and time 3.5 Consumer supply this digital 35 Andi, don&#x27;t before So the sickness it is 2 45 My

Alix Segil · Answer

Hey, guys. And welcome to New Marie. A fantastic tool and resource to help you master any topic in the stem field. My name is Alex, and today I will be helping you through a real life scenario. Algebra problem. All right, let&#x27;s get started. So as you can see, who is our problem? The gas mileage am in mill girl off a car is modeled by M equals and divided by G, where n is the number of miles driven and G is the number of gallons of gas used. And as you can see, we have two parts to this problem are a in part B. Let&#x27;s start with car, eh? Okay, our day bet way this But when given a work problem is the highlight or underlined the most important valuables and information. So it find the gas mileage M for a car that drove drawing for 40 miles on eight gallons of gas. So already we have three variables that stand out. Plus, we have m when you&#x27;re ready. Here we have m. We have end and we have G and we can see this from off pop. Right here. The gas mileage in Mill Girl of a car is modeled by Emmett Equals n divided by G Where end See, it already tells us what Venice and is the number of miles driven and G is the number of gallons of gas used. So from this information with Intel that M equals the gas mileage travel. Abbreviate GM end equals the number of miles driven. So I&#x27;m just gonna write miles dripping and G You can guess that is the number of gallons of gas use. Something&#x27;s going right, Jeanne Um, you two. That way you can tell that it&#x27;s gowns of gas used. Yeah, now that we&#x27;ve labeled these, we can also know that we can take out of this problem and equation. And the question was actually given to us. You know what? The quickness. The equation is right here when this is modeled by m m equals n divided by G. So let&#x27;s write that down. We&#x27;ll write it right here. So am I equals and divided by G. I&#x27;m sorry. This looks like a W. Let me fix that. All right now that we have all the key parts of the problem, Highlight didn&#x27;t underlined. Let&#x27;s break it down. So ask yourself. What are we trying to find? What are we trying to find out? What we&#x27;re going to find out is gas mileage, which we know is represented by the variable M. So if you forget, we have it right here, do it in blue. We have gas mileage, and this is in the problem. But in part A, we could define the gas mileage M okay, but we already know our end n G variables. And in red equals 240 And in blue G is eat. No, it&#x27;s up to you are variables for numbers formula should now look like this. It&#x27;s now we should have and equals 240 which is our a divided by G, which is eight now. It&#x27;s a simple division problem. What is 240 divided by eight. Solve that and you have your answer for gas mileage. Super simple, right? All right, let&#x27;s put apart. Be now. I&#x27;ll be So what do we need to find out? Ask yourself. I need to find out how many gallons of gas was used. If you thought that, then you&#x27;d be correct. And you already have the variables labeled from the last problem. So m we know and we know is gas mileage and and we know is number miles, German cell say number miles driven. And G you know what she is? Ji is the number of gallons used by the car. So I&#x27;m just gonna say gow used All right, now that we reiterated our variables No, nothing. So, no, what is our home and what is our equation? So we know that the m our gas mileage equals 25 and we know this because of up here, it&#x27;s in our problem. And what is our miles German? We know that our miles driven is 175. So we need to find G. No, The formula that we need to solve to solve this problem is what we used is similar to what we used in part a This equation right here we&#x27;re gonna take this and use it in part B. So let me rewrite that equation and equals and divided by G. So we know that this we know that in this problem we need to solve for G. So what, we&#x27;re gonna do this swamp that m energy? Very bills. So we have a new equation for equation will now look like this. You know, doing any red Our question will now equals g equals and provided by M. This is our new equation. And we use this. We changed the equation because now we&#x27;re finding gallons of gas used to that rg. And now we have to do a substitute. Our letters. Four numbers. So then our equation will look like G equals 1 75 provided by 25. And we know this because M equals 25 which we have here and end equals 175. Now it&#x27;s a simple division problem. Last time. So all you have to do is 175 divided by 25 then you have your G I hold is helped things.

Ankit Gupta · Answer

Sohel Ocean. Now we&#x27;re going to understand Question the ghost Mindless. I m This is a mortal as and by G, where n is number miles and is number off. Miles and G is the number of gallons number off Galan&#x27;s. Now the question is first, wasn&#x27;t it? Find the guest. My list em for a car that broke cool 40 miles on it together. And it is given to 40 miles so and 40 on the G, which is given it. So this is equal to party My by the gallon. Now be person a guard with my list I m m p equal to and by g it is m given 25 mpg and it is given and which is 1 75 My notifying Hominy gallons required Using this identity, M quoted 25 equal to and 1 75 up on So finding T, which is 1 75 upon 25 which is equal to so it This is seven gallons to this much fool. It acquired this much gas it a quack

Reese Mikesell · Answer

okay, today, we&#x27;re gonna set up in algebraic formula or an algebraic equation. So let&#x27;s say we&#x27;ve been driving in a car and we&#x27;ve been driving for T hours. He is just an arbitrary value. And we&#x27;ve been driving for T hours at 60 miles per hour. That&#x27;s what we know. But we want to try and find how far we went or are distance D That&#x27;ll be in units of Miles. But remember, we&#x27;re not trying to solve anything. We&#x27;re just trying to set up an equation. And since we&#x27;re trying to find D, that&#x27;s gonna be isolated in our equation, so everything else will be on the other side. So we&#x27;ve been driving at 60 miles per hour, four t hours, and that&#x27;s our answer. And if you want, you can check units to make sure everything works out. So let&#x27;s go ahead and do that. Our distances and miles in her speed is 60 miles per hour times T, which is in hours. So our units of time cancel and we&#x27;re left with miles, and that&#x27;s what we wanted it because we&#x27;re trying to find a distance, so that works out, and that is our answer

Taylor Shimono · Answer

this problem gives us model power equals 0.6 times feed. Cute. So we&#x27;re going to be using that for both parts of this problem. Part a tells us that if our speed is to be 12 knots, what power are we in need of in order to maintain this speed? So essentially we have r s, and we know that what we&#x27;re solving for is rp variable. So we&#x27;re going to plug that into the model that&#x27;s given to us. So, Pete, to the variable. And then we have P equals 0.6 times s, which is 12 camp. Then we&#x27;re just going to solve this equation to find what P is. And that will be her answer for part A. So the first step is going to be our exponents. So we get power equals you&#x27;re a 0.6 times 12 cubed is 1,728 and then we will play this out. We yet a power of 103 0.68 horsepower. It is necessary to move the ship at speed of 12 knots. And there&#x27;s our answer for apart, eh? So moving on to part B. We&#x27;re going to dio a very similar approach. But this time we&#x27;re plugging in our 7.5 horse powers for Pete. And we&#x27;re leaving s as are variable that we&#x27;re solving for. So this time the equation becomes 7.5 somewhere substituting for our pee right there equals 0.6 as cubed. So from right now, we&#x27;re going to isolate our answer variable. So our first step is going to be to divide both sides by I 0.6 So we&#x27;re left with s cubed equals 21 125. And then finally, to get rid of this explosion on the S, we&#x27;re going to take the cube root of both sides of the equation and we get our speed is I have not. So there&#x27;s our solution to party

Problem

Using Models Use the model given to answer the qu…

Problem 5 Medium Difficulty

Using Models Use the model given to answer the questions about the object or process being modeled.

The distance $d$ (in mi) driven by a car traveling at a speed of
$v$ miles per hour for $t$ hours is given by
$$d=v t$$
If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

Answer

245 miles

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James Stewart, Lothar Redlin, Saleem Watson

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