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Flying against a jet stream, a jet travels 4500 miles in 9 hours.
Flying with jet stream, the same jet travels 3760 in 4 hours.
What is the rate of the jet in still air and what is the rate of jet stream?
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Jet streams are some of the strongest winds in the atmosphere.
Their speeds usually range from 129 to 225 kilometers per hour (80 to 140 miles per hour),
but they can reach more than 443 kilometers per hour (275 miles per hour).
https://www.nationalgeographic.org/encyclopedia/jet-stream/#:~:text=Jet%20streams%20are%20some%20of,(275%20miles%20per%20hour).
Let u be the airplane rate in still air (in miles per hour), and
let v be the rate of jet stream.
Then the airplane's effective speed flying with the jet stream is u+v miles per hour,
while its effective speed flying against the jet stream is u-v miles per hour.
From the condition, we have this system of equations
u + v = 3760/4 = 940 mph (1)
u - v = 4500/9 = 500 mph (2)
To solve the system, add the equations. You will get
2u = 940 + 500 = 1440; hence u = 1440/2 = 720 mph.
Then from equation (1),
v = 940 - u = 940 - 720 = 220 mph.
ANSWER. The rate of the airplane in still air is 720 miles per hour;
the rate of the jet stream is 220 miles per hour.
Solved.
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It is a typical " tailwind and headwind " word problem.
See the lessons
- Wind and Current problems
- Wind and Current problems solvable by quadratic equations
- Selected problems from the archive on a plane flying with and against the wind
in this site, where you will find other similar solved problems with detailed explanations.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.