SOLUTION: Las Cruces, NM is about 600 mi from Dallas, TX. One plane flies from Dallas to Las Cruces in 1 hr 12 min, and another plane with the same air speed flies from Las Cruces to Dallas

Question 1169115: Las Cruces, NM is about 600 mi from Dallas, TX. One plane flies from Dallas to Las Cruces in 1 hr 12 min, and another plane with the same air speed flies from Las Cruces to Dallas in 1 hr 30 min.
Find the air speed of the planes and the speed of the wind.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Las Cruces, NM is about 600 mi from Dallas, TX. One plane flies from Dallas to Las Cruces in 1 hr 12 min,
and another plane with the same air speed flies from Las Cruces to Dallas in 1 hr 30 min.
Find the air speed of the planes and the speed of the wind.
~~~~~~~~~~~~~~

Let u be the plane speed at no wind. 

Let v be the speed of the wind.



The effective speed of the plane with the wind is

    u + v =  = 500 mph.    (1)    (here    represents   of an hour, or 1 hr 12 min)



The effective speed of the plane against the wind is

    u - v =  = 400 mph.    (2)    (here    represents   of an hour, or 1 hr 30 min)



From equations (1) and (2), the speed of the plane at no wind is   = 450 mph.



Then from equation (1), the speed of the wind is  500-450 = 50 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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