SOLUTION: A student group flies to Cancun for spring break, a distance of 1200 miles. The plane used for both trips has an average cruising speed of 300 miles per hour in still air. The trip

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Question 1115209: A student group flies to Cancun for spring break, a distance of 1200 miles. The plane used for both trips has an average cruising speed of 300 miles per hour in still air. The trip down is with the prevailing winds and takes ( one hour and a half) less than the trip back, against the same strength wind. What is the wind speed?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
1200%2F%28300-r%29 - 1200%2F%28300%2Br%29 = 3%2F2


2400*(300+r) - 1200*(300-r) = 3*(90000-r^2)


4800r = 3*(90000-r^2)


1600r = 90000 - r^2


r^2 + 1600r - 90000 = 0.


r%5B1%2C2%5D = %28-1600+%2B-+sqrt%281600%5E2+%2B+4%2A90000%29%29%2F2 = %28-1600+%2B-+1708.8%29%2F2.


The positive solution is  r = 54.4.


Answer.  54.4 miles per hour.


Check.   1200%2F%28300-54.4%29+-+1200%2F%28300%2B54.4%29 = 1.5 hours.    ! Correct !

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It is a typical and standard "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.


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.