Problem: Cars and travel the same distance. Car travels half that distance at miles per hour and half at miles per hour. Car travels half the time at miles per hour and half at miles per hour. The average speed of Car is miles per hour and that of Car is miles per hour: Then we always have
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Solution:
Let denote the distance. The time for car is and the average speed is
For car , let denote the diatance at speed reapectively so that if the time for car is and . Adding these and the average speed of car is
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The fact that for positive and follows trom .