An airplane takes off from Reagan National Airport’s (DCA) Runway 1 (that is, a

Question

An airplane takes off from Reagan National Airport’s (DCA) Runway 1 (that is, a heading of 10 East of North), headed for Chicago’s O’Hare (ORD) airport. The bearing from DCA to ORD is 155.8 and it is 982.6km between the two airports. This airplane (an Airbus A319) has a cruising speed of 825km/h. At the cruising altitude of 10,000m there is a southeasterly wind, bearing 45, at 8m/s. (Winds are named for the direction from which they are blowing. Be careful when writing out this vector.) If you assume that the moment the airplane leaves the runway in Virginia it is at it’s cruising altitude and velocity, what heading should the pilot take to get to Chicago fastest? How long will this trip take?

Here's what I have so far:

I don't know what else to do.

Explanation / Answer

Did you see my comment from yesterday? There is something amiss with the wind vector. A southeasterly wind blows towards the northwest, which would be a bearing of 315 degrees. A wind that is blowing with a bearing of 45 degrees is out of the southwest. The descriptions of the wind are inconsistent.

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