Joe flies a plane 300 miles in 2 hours to a destination with the wind. On the return trip against the wind, he only flies 270 miles in 2 hours. Assuming wind speed is constant, what's the wind speed?

Jonas Huff

Jonas Huff

Answered question

2022-11-11

Joe flies a plane 300 miles in 2 hours to a destination with the wind. On the return trip against the wind, he only flies 270 miles in 2 hours. Assuming wind speed is constant, what's the wind speed?

Answer & Explanation

dobradisamgn

dobradisamgn

Beginner2022-11-12Added 17 answers

Let's think of the problem this way:
On the first leg of the trip , Joe flew 300 miles in 2 hours. We can then say that he flew:
300 miles 2 hours = 150 m p h
Since this was in the same direction of the wind, the plane was going the speed of the plane in still air plus the speed of the wind:
Airplane speed + wind speed=150mph
On the return trip, Joe flew 270 miles in the same 2 hours. We can say that he flew:
270 miles 2 hours = 135 m p h
Since this was in the opposite direction of the wind, the plane was going the speed of the plane in still air minus the speed of the wind:
Airplane speed − wind speed=135mph
Putting it together
We can add the two equations:
Airplane speed + wind speed = 150 m p h
Airplane speed - wind speed = 135 m p h ̲
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
2 × Airplane speed = 285 m p h
Which means that Airplane speed = 285 2 = 142.5 m p h
The wind speed is then: 142.5 + wind speed = 150 wind speed = 7.5 m p h

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