It is known that homing pigeons fly faster over land than over water. Assume they fly 10 meters per second over land but only 8 meters per second over water. If a pigeon is located at the edge of a straight river 500 meters wide and must fly to its nest, 1300 meters away on the opposite side of the river, what path would minimize its flying time? Be sure to justify that you have found the minimum flying time.

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