Question 309028: a pilot can fly an airplane 2160 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 30 miles per hour, find the speed of the plane in still air.
Answer by mollukutti(30)   (Show Source):
You can put this solution on YOUR website! Basic facts:
1. The speed of the airplane will always be greater than the wind.
2. When the airplane travels with the wind, the speed of the wind will be added to its own speed.
3. When the airplane travels against the wind, the speed of the wind will be subtracted from its own speed
Now let us try to solve the problem.
Let us take the speed of the airplane in still air as x miles/hr
We have the speed of the wind at 30 miles/hr
So when the airplane is moving in the direction of the wind the combined speed will become (x + 30)miles/hr
When the airplane is moving against the wind the combined speed will become
(x - 30)miles/hr
Let us take the help of the formula:
TIME taken = Distance travelled / Speed
Time taken to travel with the wind = 2160/(x + 30)
Time taken to travel against the wind = 1920 / (x-30)
We know from the question that the time taken is same in both directions, hence we can form the equation:
2160/(x + 30) = 1920 / (x-30)
or, (x-30)/(x + 30)= 1920 / 2160 (cross multiplication)
or, (x-30)/(x + 30)= 8/9 (reduced to lowest terms)
or, (x-30)x 9 = 8 x (x + 30) (cross multiplication)
or, 9x - 270 = 8x + 240
or, 9x - 8x = 240 + 270 (Bringing variables to one side and numbers to the other)
or, x = 510
Hence the speed of the airplace in still air is 510 miles/hr
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