Jet travels against and with wind

Question

jet travels 6543 miles against the wind in 9 hours and 7263 miles with the wind in the same amount of time what is the rate of the jet in still air and what is the rate of the wind?

Answer 1

Let V = still air speed of jet and W = speed of the wind.

When flying AGAINST the wind, in 9 hours the jet travels 6543 miles. Symbollically this is 9*(V-W) = 6543.

Simplify to get V-W = 6543/9 = 727 mph.

When flying WITH the wind, in 9 hours the jet travels 7263 miles. Symbolically this is 9*(V+W) = 7263.

Simplify to get V+W = 7263/9 = 807 mph.

Add the two simplified equations together to find V, the still air speed of the jet:

2V + W - W = 1534. Divide both sides by 2 to get V = 767 mph.

Use this value in either equation to find W. 767+W = 807. Subtract 767 from both sides to get W = 40mph.

The still air speed of the jet is 767 mph and the speed of the wind is 40 mph.