Problem

Aviation. An airplane can fly with the wind a dis…

02:06

Problem 42 Hard Difficulty

The Jet Stream. The jet stream is a strong wind current that flows across the United States, as shown above. Flying with the jet stream, a plane flew $3,000$ miles in 5 hours. Against the same wind, the trip took 6 hours. Find the speed of the plane in still air and the speed of the wind current.

Answer

$w=50$

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Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 4

Problem Solving Using Systems of Equations

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Video Transcript

so Okay, Similar. There's a maps there with the jet stream on it. Flying with the jet stream. You're gonna go faster. So 3000 miles in five hours. So with gives us 3000 miles in five hours, 3000 miles, five hours against. They said that the return trip took six hours. So you have Thio kind of think logically here. That's gonna be a return trip. So it's the same distance of 3000 miles. Um, we need to figure out the speed of the plane in the air and the speed of the current. Let's just say X equals plane. And then why equals the current? And the basic idea we're gonna use is just that distance, Equal speed time? Fine. I'm not going to use the letters. D r a. T. I mean, he's the information of the problem, but its distance is speed. Times time. This is with the current 3000 miles is a speed x plus. Why? Because the current is making the plane go faster, so you add them together, multiply by five hours against the jet stream. Would be 3000 miles be. That's against it. Yet to subject X minus Y times six. One option here is to distribute. Ah, kind of nice trick you can do instead of distributing is you can just divide both sides by five. Divide both sides by six. That gets rid of the five in the six outside of the parentheses. You don't even need to do distributive property. It's a 3000 divided by five is 606 100 equals X plus wire, then on the second equation, divided by six. So I have 500 equals x minus. Y not be able to just figure out that it's in the middle. Um, but let's just go through inshore steps. If we add those two things together, the Y values they're gonna eliminate, we'll have 1100 equals two acts and divided by two tells us that axis 5 50 because we knew X Plus Y was 600. We know that why 50 and you can check it with the other equation X minus Y works so the plane can fly 5 50

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