Difference between revisions of "2009 AMC 8 Problems/Problem 14"
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==Solution 2== | ==Solution 2== | ||
− | + | We calculate the harmonic mean of Austin and Temple. | |
Plugging in, we have: <math>\frac{2ab}{a+b} = \frac{2 \cdot 60 \cdot 40}{60 + 40} = \frac{4800}{100} = \boxed{\textbf{(B)}\ 48}</math> miles per hour. | Plugging in, we have: <math>\frac{2ab}{a+b} = \frac{2 \cdot 60 \cdot 40}{60 + 40} = \frac{4800}{100} = \boxed{\textbf{(B)}\ 48}</math> 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 = <math>\boxed{\textbf{(B)}\ 48 } \qquad</math> | ||
+ | -themathgood | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/CnWuadfT3xA Soo, DRMS, NM | ||
+ | |||
+ | https://www.youtube.com/watch?v=-O5zQT9mp2I ~David | ||
==See Also== | ==See Also== |
Latest revision as of 20:23, 20 March 2024
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) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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