SOLUTION: A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against

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Question 1186288: A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. Find the speed of the wind.


Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
speed with the wind is 200+w
speed against the wind is 200-w
takes 500/(200+w) hours with the wind
takes 300/(200-w) hours against the wind
those are equal
cross multiply,
100000-500w=60000+300w
40000=800w
w=50 mph
250 mph with wind = 2 hours for 500 mi.
150 mph against wind = 2 hours for 300 mi.

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
A plane has a cruising speed of 200 miles per hour when there is no wind.
At this speed, the plane flew 500 miles with the wind in the same amount of time
as it flew 300 miles against the wind. Find the speed of the wind.
~~~~~~~~~~~~~~~~~ 

Let x be the speed of the wind, in miles per hour.


Then the plane's effective speed flying with the wind is (200+x) mph;

                 effective speed flying against the wind is (200-x) mph.


Now we write the "time" equation


    500%2F%28200%2Bx%29 = 300%2F%28200-x%29


To solve it, first cross-multiply; then simplify and find x


    500*(200-x) = 300*(200+x)

      5*(200-x) =   3*(200+x)

    1000 - 5x   =   600 + 3x

    1000 - 600  =   3x  + 5x

        400     =     8x

         x      =  400/8 = 50.


ANSWER.  The speed of the wind is  50  miles per hour  (rounded).


CHECK.   500%2F%28200%2B50%29 = 2  hours with the windth.

         300%2F%28200-50%29 = 2 hours against the windth.    ! The flying time is the same:  CORRECT !

Solved.