Question 966100


Let  x  be the wind speed (=rate),  in {{{miles/hour}}}.

Then the speed of the plane when flying with the wind is  215 + x  {{{miles/hour}}}.

The speed of the plane when flying against the wind is  215 - x  {{{miles/hour}}}.

The plane covers the distance of  750  miles in  {{{750/(215 + x)}}}  flying with the wind.

The plane covers the distance of  540  miles in  {{{540/(215 - x)}}}  flying against the wind.


So,  you have an equation  {{{750/(215 + x)}}} = {{{540/(215 - x)}}} to find  {{{x}}}. 


Multiply both sides by  {{{(215 + x)*(215 - x)}}}.  You will get 


750*(215-x) = 540*(215+x). 


Divide both sides by  30.  You will get 


25*(215-x) = 18*(215+x).


Open parentheses;  collect the  x-terms in the right side;  collect the constant terms in the left side:


25*215 - 18*215 = 18*x + 25*x,  or


7*215 = 43x.


Divide both sides by 43.  You will get 

x = 7*5 = 35.


<B>Answer</B>. The rate of wind is &nbsp;35 {{{miles/hour}}}.