SOLUTION: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed fo the plane

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Question 128085: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed fo the plane in still air.
Answer by Ganesha(13) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speeds of plane in still air and the wind be x and y miles respectively.
Then the speeds of the plane along and against the wind are x+y and x-y respectively.But these actuals are given to be 500m/h and 400m/h respectively. Therefore, you can solve the two unknowns x and y . Therefore,
x+y = 500---(1)
x-y = 400---(2)

Adding (1) and (2) to get 2x = 900 ==>
x = 900/2 =450 miles/h
Substitute this value of x in (1) to get y= 500-450 = 50miles/h.
Thus x=450 is the plane speed in still air. y = 50 is the wind speed.
NB: If the speed of wind is 10 mph, the conditions become too many violating the nature's independence. You cannot have the independence of cutting the cord at two places and have your own independence of telling the length also!