Solve each problem. See Example 2. Elwyn averaged 50 mph trave...

Question

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Table showing rates and times for a round trip: 50 mph for x hours going, 55 mph for 32 minus x hours returning.

Accepted Answer

Welcome back. I am so glad you're here. We have this student and he went from home with drama, lovely home here. He's got a chimney to his school. Can draw a school over here, label it school via route A. Here can be route A at a speed or in other words, a rate, the rate of route A of 30 MPH. That is slow. Alright, while returning home, he has taken a different route, we can call this route B of the same distance. Okay. Well, we know now that the distance of route A is the same as or equals the distance of route B and we can say that those both equal the distance because they're the same thing. The distance of route A equals the distance of route B which equals the distance this time. So on route B, his speed or his rate, The rate of route B was equal to 35 mph. He sped up a little bit, find the distance between the school and his house. Alright. We're looking for di we want di equals something, Find the distance between the school and his house if he took a total of 26 hours of travel. That is commitment at those speeds. All right. So we know that the time of route a plus the time of route B Together equal 26 hours. Okay. Well, what else do we know? We know we have distance rate and time and we recall from previous lessons that when we're dealing with distance rate and time, we can use the distance formula, distance equals rate times time. So let's set up a distance formula for route A and for route B for route A, we're going to just use D for distance because we know that's the same as the distance of route A distance equals the rate. So the rate of route is going to be 30 MPH times the time. And we don't know what the time of route A is. We only know what it is in relation to route B and that together they equal 26 miles, 26 hours. So we've got a formula there. Now let's set up a formula for route B. So again, it's going to be distance equals and the rate for route B is 35 MPH times the time of route B. We don't know what that is. We just label it time of route B And now we can get both of these distance formulas so that they're solved for time. And then we can use substitution and plug them into this formula time of route a plus time of route B equals 26. So let's solve for time for the first one distance equals 30 times the time of route, they will divide both sides by 30. And we get That the time of route a equals distance over 30. So we can substitute distance over 30 for the time of route a. Alright, next, let's work on solving for the time of route B. We will take both sides and divided by 35 to get the time of route B by itself. And we get a formula of the time of route B equals distance divided by 35. And we'll substitute distance over in for the time of route B. Now, we can bring this down that they're added together and together they equal 26 hours. Now we just need to solve for D which is what we're looking for. Wonderful, okay, solving for D we've got these fractions, we want to get rid of the fractions. So let's multiply everything by the common denominator of 30 and 35 which is 210. So we'll have 210 times d over 30 plus times d over And that equals 26 times 210. So now simplifying, we can take 210 divided by 30 and 210 divided by equals seven. So that's 70 And 210 divided by 35, that equals six. So this is plus six, d equals 26 times 210 equals 5460. We can combine like terms on the left hand side, seven D plus six D equals 13 D that still equals 5460. To get the d by itself, we can divide both sides by 13 And we get d equals 5460 divided by is 420. So d equals 420. The distance one direction from his house to his school is 420 miles. That is commitment. Alright. We look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Key Concepts

Distance-Speed-Time Relationship

Average Speed and Different Routes

Setting Up and Solving Algebraic Equations

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