Question 431703
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One plane traveled 800 miles in the same time a second plane traveled 1,000 miles. 
The rate of the second plane was 50 mi/h faster than the rate of the first plane. 
How fast did each plane fly?
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        Calculations in the post by @mananth are irrelevant to the given problem in the post.

       I came to provide a correct solution.



<pre>
Plane A x     800 miles

Plane B x+50 1000 miles


Write time equation, saying that the fly time is the same in both cases


    {{{800/x}}} = {{{1000/(x+50)}}}


To solve it, cross multiply; then simplify

    800*(x + 50) = 1000*x

    8*(x + 50)   = 10*x

    8x + 400     = 10x

    10x - 8x     = 400

       2x        = 400

        x        = 400/2 = 200.


<U>ANSWER</U>.  One plane speed is 200 mi/h;  the other plane speed is 200+50 = 250 mi/h

         Make a check to assure that the answer is valid.
</pre>

Solved.