SOLUTION: If a plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind, find the speed of the plan without a wind and speed with the wind.

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Question 1048168: If a plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind, find the speed of the plan without a wind and speed with the wind.
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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If a plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind,
find the speed of the plan without a wind and speed highlight%28cross%28with%29%29 of the wind.
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If "u" is the plane speed without a wind and "v" is the speed of the wind, then

1.  The speed of a plane relative to the Earth (relative to the ground) is 

    u + v when it flying with the wind,  and
    u - v when it flying against the wind.


2. So, you are given 

   u + v = 500,   (1)
   u - v = 400.   (2)


3.  Add these two equations. You will get

    2u = 500 + 400  --->  2u = 900  --->  u = 900%2F2 = 450

         Thus you just found the speed of the airplane at no wind. It is 450 miles per hour.

    Now you will easily find from (1) v = 500 - 450 = 50.

        So, the speed of wind is 50 mph.

Answer.  The speed of the airplane at no wind is 450 miles per hour.
         The speed of wind is 50 mph.