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Gerry just returned from a cross-country trip. The trip was 3,000 miles from his home, and his total time in the airplane for the round trip was 11 hours. If the plane was flying at a rate of 550 miles per hour, what was the speed of the jet stream?

User Mhyfritz
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2 Answers

6 votes

Answer:

50 mph

Explanation:

This is a uniform motion situation. A diagram will help us visualize the situation.

Diagram of plane in motion with and against the wind

Diagram first shows motion of the plane at 550 miles per hour with an arrow to the right. The plane is traveling 3000 miles with the wind, represented by the expression 550 plus r. The jet stream motion is to the right. The round trip takes 11 hours. At the bottom of the diagram, an arrow to the left models the return motion of the plane. The plane’s velocity is 550 miles per hour, and the motion is 3000 miles against the wind modeled by the expression 550 – r.

We fill in the chart to organize the information.

We are looking for the speed of the jet stream.

Let r= the speed of the jet stream.

When the plane flies with the wind, the wind increases its speed. So, the rate is 550+r.

When the plane flies against the wind, the wind decreases its speed. So, the rate is 550−r.

Write in the rates. Write in the distances. Since D=r⋅t, we solve for t and get t=Dr. We divide the distance by the rate in each row and place the expression in the time column.

Type Rate

Time

=

Distance

Headwind

550−r

3,000550−r

3,000

Tailwind

550+r

3,000550+r

3,000

11

We know the times add to 9. So, we write our equation.

3,000550−r+3,000550+r=11

We multiply both sides by the LCD.

(550−r)(550+r)(3,000550−r+3,000550+r)=11(550−r)(550+r)

Simplify.

3,000(550+r)+3,000(550−r)=11(550−r)(550+r)

Factor out the 3,000.

3,000(550+r+550−r)=11(5502−r2)

Solve.

3,000(1100)=11(5502−r2)

Divide by 11.

3,000(100)=5502−r2

Simplify.

300,000−250050=302,500−r2=−r2=r

Check.

Is 50 mph a reasonable speed for the jet stream? Yes.

If the plane is traveling 450 mph and the wind is 50 mph,

tailwind 550+50=600 mph 3,000600=5 hours

headwind 550−50=500 mph 3,000500=6 hours

The times add to 11 hours, so it checks.

The speed of the jet stream was 50 mph.

User Cdmdotnet
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7.7k points
2 votes

The speed of the jet stream is 4.55 miles per hour

Explanation:

Distance of one way trip= 3000 miles

The total distance of the round trip= 6000 miles

Total time = 11 hrs

Speed of the plane = 550 miles per hr

Speed = distance/time

= 6000/11

= 545.45 miles per hour

Speed of the plane = 545.45 + speed of the jet stream

550 = 545.45 + speed of jet stream

Speed of jet stream = 4.55 miles per hour

The speed of the jet stream is 4.55 miles per hour

User My Work
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