Puzzle for March 23, 2010

The airplane I flew to Chicago in flew eastward at 37,000 feet. Turns out that east-bound flights typically fly at odd altitudes and west-bound flights travel at even altitudes (38,000 feet in this case). They use these altitudes to help keep the airplanes separated as they travel the "sky lanes" over the United States.

So an obvious question for today: how high are the planes flying (in miles) and how far apart are two planes flying over the "same spot"?

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