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Problem of the Week 1200

Flying in Circles

An airplane flies at a constant air speed of 145 mph in a horizontal plane directly above a flat circular track of radius 10 miles. Throughout the flight, the wind blows in a fixed direction and at a sustained speed w, where w < 145.

If the travel time around the track is 30 minutes, find the wind speed in miles per hour.

Extra Credit: Solve the travel time problem given the wind speed. If the air speed is v, the track radius is r, and the constant wind has speed w < v, find the time required for the plane to complete one circuit.

The idea here is to give as close to a closed-form for the time as possible. There appears to be an elegant formula.

Source: John Snyder, based on a problem he saw at a Purdue University problem site.

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29 January 2015