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 30 minutes. What is the plane's speed in still air, and how fast is the wind blowing?
Let the speed of the plane be X mph
If flying with the wind (tailwind) then it is assisting you,
if flying against the wind (headwind) then it is slowing you down
The distance and the speed of the plane remain constant in this equation.
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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:
written as: x - wind speed = 180 miles in 2 hr.
x - wind speed = 180 / 2 = 90mph
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On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 30 minutes.:
written as x + wind speed = 180 miles in 1.5 hr
x + wind speed = 180 /1.5 = 120 mph
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x - wind speed = 90mph
x + wind speed = 120 mph
120 - 90 = 30 / 2 trips = 15mph wind speed
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check :
x - 15 = 90mph ; x = 90 +15 = 105 plane speed
x + 15 = 120 mph; x = 120 - 15 = 105 plane speed