Question 1142254
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<pre>
If x is the speed of the plane at no wind (in miles per hour), then

    the effective ground speed with the wind is (x+20) mph, while 

    the effective ground speed against the wind is (x-20) mph.


The "time" equation then is


    {{{1050/(x+20)}}} = {{{850/(x-20)}}},


according to the condition   (same amount of time for each flight).


To solve it, cross multiply and simplify


    1050*(x-20) = 850*(x+20)

    1050x - 1050*20 = 850x + 850*20

    1050x - 850x = 850*20 + 1050*20

    x = {{{(850*20 + 1050*20)/(1050-850)}}} = 190.


<U>ANSWER</U>.  The speed of the plane at no wind is 190 miles per hour.


<U>CHECK</U>.   {{{1050/(190+20)}}} = {{{1050/210}}} = 5 hours;   {{{850/(190-20)}}} = {{{850/170}}} = 5 hours.    ! Correct !
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Solved.


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<U>The lesson to learn from this solution and the things to memorize are</U> :


<pre>
    1.  The effective speed of a plane flying with    a wind is the sum        of the two speeds.

    2.  The effective speed of a plane flying against a wind is the difference of the two speeds.

    3.  It gives you a "time" equation, which you easily can solve and find the unknown plane' speed.
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