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Dr. Worm leaves his house at exactly 7:20 a.m. every morning. When he averages 45 miles per hour, he arrives at his workplace five minutes late. When he averages 63 miles per hour, he arrives five minutes early. What speed should Dr. Worm average to arrive at his workplace precisely on time?

 Dec 31, 2021
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When the distance is fixed and the speeds are known, the easiest solution is to take the "harmonic mean" of the 2 speeds:

 

[2 x 45 x 63] / [45 + 63] ==5,670 / 108 ==52.50 mph -the average speed to arrive on time.

 

Note: You can do it the long way by using: Average speed==Total distance / total time.

You should, however, get the same result.

 Dec 31, 2021

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