I will post a challenging math problem each day. The level of difficulty will vary, but most problems should not require any specialized knowledge beyond calculus. Problems are also posted on Twitter using the hashtag #mathpotd.
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?
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.
Answer: 120 mph.
ReplyDeleteLet 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.