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.
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<pre>
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 = {{{600/((6/5))}}} = 500 mph.    (1)    (here  {{{6/5}}}  represents  {{{6/5}}} of an hour, or 1 hr 12 min)



The effective speed of the plane against the wind is

    u - v = {{{600/((3/2))}}} = 400 mph.    (2)    (here  {{{3/2}}}  represents  {{{3/2}}} of an hour, or 1 hr 30 min)



From equations (1) and (2), the speed of the plane at no wind is  {{{(500+400)/2}}} = 450 mph.



Then from equation (1), the speed of the wind is  500-450 = 50 mph.
</pre>

Solved.


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It is a typical "tailwind and headwind" word problem.


See the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-plane-flying-with-and-against-the-wind.lesson>Selected problems from the archive on a plane flying with and against the wind</A> 

in this site, where you will find other similar solved problems with detailed explanations.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the section "<U>Word problems</U>", &nbsp;the topic "<U>Travel and Distance problems</U>".



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.