<PRE><B>Question 585408</B>
Let the speed of the wind be w miles per hour.
Let t be the time taken by pilot to travel 560 miles with the wind and also to travel 360 miles against the wind.

Case:  When traveling with the wind, 

total speed of pilot = speed of pilot in still air + speed of wind
Vt =  230 + w

Distance traveled = total speed * time taken
560 = (230 + w)* t
 {{{ t= 560/(230+w) }}}  ------------ (1)


Case: When traveling against the wind,

total speed of pilot = speed of pilot in still air - speed of wind
Vt = 230 - w

Distance traveled = total speed * time taken
360 = (230 - w)* t
 {{{ t= 360/(230 - w) }}}  -------------  (2)


Using equation (1) and (2),

{{{ 560/(230 + w) = 360/(230 - w) }}}
{{{ 14/(230 + w) = 9/(230 - w) }}}    { Dividing both the sides by 40 }
{{{ 14*(230 - w) = 9* (230 + w) }}}   { Cross-multiplication}
     3220 - 14w =  2070 + 9w
     3220 - 2070  = 14w + 9w
     1150 = 23w
      w = 1150/23
      w = 50 

Hence, the speed of the wind is 50 miles per hour.

Hope this helps~!
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