SOLUTION: An airplane can travel 395mph in still air. If it travels 1242 miles with the wind in the same length of time it travels 1128 miles against the wind, what is the speed of the wind?

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Question 1134644: An airplane can travel 395mph in still air. If it travels 1242 miles with the wind in the same length of time it travels 1128 miles against the wind, what is the speed of the wind?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
The "time equation" is


1242%2F%28395%2Bw%29 = 1128%2F%28395-w%29.


Solve for w, which is the wind speed - the value under the problem's question.


Start cross-multiplying.   Then every next step after that is OBVIOUS.


Happy calculations !

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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.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane can travel 395mph in still air. If it travels 1242 miles with the wind in the same length of time it travels 1128 miles against the wind, what is the speed of the wind?
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w = windspeed
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1242/(395 + w) = 1128/(395 - w)
Cross multiply
1242*(395-w) = 1128*(395+w)
1242*395 - 1242w = 1128*395 + 1128w
114*395 = 2370w
w = 19 mi/hr
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PS Planes use knots, not mi/hr
Boats also use knots.
Knots are units of speed. 1 knot = 1 nm/hr, 1 nautical mile per hour.
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That does not affect the answer or the calculations, but it's another example of people writing math problems who do not know the subject.
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Buildings and universities use mi/hr, km/hr and other units, but planes use knots.
No building or institution has ever filed a flight plan and left the ground.