Problem of the Week

A question this week, inspired by the Olympics, from Professor Ollie Nanyes.

A common lament of a long distance runner is that, as time goes on, the finish line never seems to get any closer. Consider the plight of an out-of-shape Bradley mathematics professor as he plods along a race route at a 10 minute per mile pace. He sees the finish line along his "line of sight".  Although the finish line is only two miles away from the starting line as the crow flies, it lies on the opposite side of a hemispherically shaped canyon and the professor's route goes there along a "great circle" which passes through the very bottom of the canyon. See figure below.  He maintains his steady 10 minute per mile pace throughout.

In terms of his "line of sight" distance to the finish line, at what pace is he closing in on the finish line?

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©MM Alberto L. Delgado