SOLUTION: New York City and Houston are 1600 miles apart. Because the jet stream blows towards the East, flights from Houston to New York take 1/2 an hour less than flights from New York to

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Question 1117087: New York City and Houston are 1600 miles apart. Because the jet stream blows towards the East, flights from Houston to New York take 1/2 an hour less than flights from New York to Houston. If a commercial jet flies 520 MPH how fast does the jest stream blow?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let v be the rate of the jet stream, in miles per hour.


Then the effective speed of the plane flying with the wind is (520+v) mph, and the time of the flight with tailwind is 1600%2F%28520%2Bv%29 hours.


    The effective speed of the plane flying against the wind is (520-v) mph, and the time of the flight with headwind is 1600%2F%28520-v%29 hours.


The time difference is  1%2F2  of an hour,  which gives you an equation

1600%2F%28520-v%29 - 1600%2F%28520%2Bv%29 = 1%2F2.


To solve it, multiply both sides by  2*(520-v)*(520+v).  You will get

2*1600*(520+v) - 2*1600*(520-v) = (520-v)*(520+v)

2*1600*v + 2*1600*v = 520^2 - v^2

v^2 + 6400v = 520^2

v^2 + 2*3200 + 3200^2 = 520^2 + 3200^2

%28v+%2B+3200%29%5E2 = 10510400

v + 3200 = +/- sqrt%2810510400%29

v = - 3200 + 3241.975 = 41.975.


Check.  1600%2F%28520-41.975%29 - 1600%2F%28520%2B41.975%29 = 0.5.   ! Correct !


Answer.  The rate of the jet stream was  41.975 mph.

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.


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I agree with the @Alan's note that the geographical settings in this problem are FAR from to be perfect.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
depends on the headings of the plane between the 2 cities.
It can be solved IF and only IF the plane's headings are given.
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People who don't understand things should not attempt to write math problems about them.