Question 264864
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an airplane travels 900 miles from Houston to Miami in 6 hors against the wind. 
on its return trip, with the wind, it takes only 5 hours. 
find the rate of the airplane with no wind. find the rate of the wind
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        The solution in the post by @mananth is correct: it leads to correct answer.

        But the @Mananth' solution is badly organized.


        One of the goals of such problems is to teach students to present their solution in perfect 

        form with straightforward logic.


        Therefore I place my solution here.



<pre>
Let the ground speed be x
And the wind   speed be y


AGAINST WIND

Distance = 900 miles.
Rate = Distance/time
x-y = 900/6 = 150 miles per hour.


WITH WIND

Distance = 900 miles.
Rate = Distance/time
x + y = 900/5 = 180  miles per hour.


Thus we have a system of two equations for unknowns x and y

    x - y = 150    (1)
    x + y = 180    (2)


To find 'x', add the equations.  You will get

    2x = 150 + 180 = 330  --->  x = 330/2 = 165.


To find 'y', substitute x = 165 in equation (2)

    165 + y = 180  --->  y = 180 - 165 = 15.


<U>ANSWER</U>.  The rate of the plane with no wind is 165 miles per hour.

         The rate of the wind is 15 miles per hour.
</pre>

Solved.