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A man flies a small airplane from Fargo to Bismarck, North Dakota

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 hour and 12 minutes. What is the plane's speed in still air, and how fast is the wind blowing?

his plane speed equals mph?
the wind speed equals mph?

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1 Answer

First, convert the time of the second flight to hours.  1 hour 12 min = 1.2 hours.

The plane's ground speed from Fargo to Bismarck is 180 / 2 = 90 mph, and the plane's ground speed on the return trip is 180 / 1.2 = 150 mph.  From these figures, we can determine that the plane's ground speed in still air is (150 + 90) / 2 = 120 mph, and the wind speed is (150 - 90) / 2 = 30 mph.  Assume the direction of the wind has not changed.