Sunday, September 20, 2009

Road Trip

Sue drives from San Francisco to New York City. At the halfway point her average speed is 40 miles per hour. How fast must she drive to average 60 miles per hour for whole trip?
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  1. DavidSeptember 20, 2009 at 6:49 PM

    Answer: 120 mph.

    Let t be the time in hours for Sue to reach the halfway point. The distance from San Francisco to the halfway point is 40t miles, so the total distance is 80t miles.

    If Sue averages 60 mph during the entire trip, then the total time is 80t/60 = 4t/3 hours. Since she used t hours to reach the halfway point, she has only t/3 hours remaining to complete the trip, and she must maintain an average speed of 40/(t/3) = 120 mph.

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