.
Let u be the speed of the plane in still air and v be the jetstream speed.
Then
u - v = = 561 (1)
is the equation for the plane' speed traveling against a jetstream.
u + v = = 671 (2)
is the equation for the jet speed traveling with a jetstream.
To find u from these equations, add them. You will find
2u = 561 + 671 = 1232 ========> u = 1232/2 = 616 miles per hour is the plane speed in still air. ANSWER
Then from (2) v = 671 - 616 = 55 miles per hour is the jetstream speed. ANSWER
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.