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.