Problem

The distance from Jackson to Lodi is about $40 \m…

Problem 28 Easy Difficulty

Vera Koutsoyannis flew her plane for 6 hr at a constant rate. She traveled $810 \mathrm{mi}$ with the wind, then turned around and traveled $720 \mathrm{mi}$ against the wind. The wind speed was a constant $15 \mathrm{mph} .$ Find the rate of the plane.

Answer

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Precalculus

Algebra

Beginning and Intermediate Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 4

Equations Quadratic in Form

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Video Transcript

we've got a plane flying with or against the wind. I'm going to be calling the planes Speed X and the wind speed. Why now We know that if the plane flies with the wind like in the picture here, it will have a speed of X plus y. That is its speed plus the wind speed. And we know that in five hours it could go 800 miles. So, as you know, from the book speed times time is equal to distance. Thus we have speed expose. Why times time. Five hours equals 800 miles. We also know that if the plane turns around and goes the other way against the wind, it will have the new speed of X minus y. And it takes eight hours to go 800 miles. All right, so with this in mind, let's determine what X and y are. So looking at this, the first thing I want to do is actually set these equations equal to each other. They're both equal to 800. So because of this, we can say X plus y times five equals eight times x minus y all right. So with this in mind, let's distribute out the five and the eight. This will US five X plus five y equals eight X minus eight. Y all right now we can cancel out some terms by adding all of the wise, the left side and subtracting on the X is to the right. So we will now have 13. Why equals three X and finally dividing across by three will give us X. By itself. X equals 13. Why over three now 13 y ver three isn't a very nice looking term. However, we can make this look a little bit better in time. So when I'm next, going to do is plug this into one of our equations. Specifically, we had the equation of five X plus five y equals 800. Now, this was just the first equation right here with the five distributed out. So now I'm going to plug in X into this. And so we get So X was 13. Why over three giving us five times 13. Why, over three plus five y equals 800. All right, now that we have that five times 13 whatever. Three plus five, why is a bunch of fraction edition and we have to do some common denominator finding that's a long process. But when you finally complete that, you will end up with 80 y Over three equals 800. Okay, now we can multiply across by three and divide by 80 in that which is just getting rid of the coefficient of why which will give us that. Why is equal to 30. All right now we know what why is. That's the wind speed 30 MPH. And with that, we can figure out X. So if five acts plus five y equals 800 and why equals 30 we have five X plus five times 30 or 1 50 equals 800. Now we can subtract 1 50 from 800. Giving us five X equals 6 50 a final division of both sides by five will give us that X is equal to 130 MPH. Thus, the plane traveled at 1 30 MPH, and the wind speed was 30 miles an hour

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