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 1.5 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 ______________ mph.

Answer 1

• Plane = 105 mph and wind = 15 mph

Explanation:

Let the plane's speed is p, the wind speed is w.

We have:

• 2(p - w) = 180 ⇒ p - w = 90
• 1.5(p + w) = 180 ⇒ p + w = 120

Solve the system by elimination, add up the equations:

• p - w + p + w = 90 + 120
• 2p = 210
• p = 105

Find the value of w:

• 105 - w = 90
• w = 105 - 90
• w = 15