A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles.

Question

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hours. What is the plane's speed in still air, and how fast is the wind blowing?

His plane speed is
mph.
The wind speed is

Answer 1

 

   R is the speed of the plane.

   S is the speed of the wind.

 

  180 = (R-S)*2  =  (R+S)*1

 

            2r - 2s = r + s

 

            2r - 2s - r - s = 0

 

            r - 3s = 0

 

           r = 3s

 

The plane is 3 times as fast as the wind.

 

Going against the wind:

 180 = (3s - s)*2

 

 180 = 2s * 2

 

 180 = 4s

 

  s = 180/4 = 45

 

The wind speed is 45 mph

The plane speed is 135 mph

 

Against the wind is 90 mph for 2 hours; that's 180 miles.

With the wind is 180 miles; that;s 180 miles in 1 hour.

 

 

180