2009 AMC 8 Problems/Problem 14
Problem
Austin and Temple are miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
Solution
The way to Temple took hours, and the way back took for a total of hours. The trip is miles. The average speed is miles per hour.
Solution 2
We calculate the harmonic mean of Austin and Temple. Plugging in, we have: miles per hour.
Solution 3
The 50 miles part of this question is redundant. We find that the average speed is skewed towards the lower speed, since you spend more time in the lower speed. So, we take the LCM of 40 and 60, getting 120. So, we do (40 + 40 + 40 + 60 + 60)/5, calculation the ratio of the parts and taking the mean. Solving, we get 240/5 = -themathgood
Video Solution
https://youtu.be/CnWuadfT3xA Soo, DRMS, NM
https://www.youtube.com/watch?v=-O5zQT9mp2I ~David
See Also
2015 Problem 17
2009 AMC 8 (Problems • Answer Key • Resources) | ||
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