Difference between revisions of "2009 AMC 8 Problems/Problem 14"
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Austin and Temple are <math> 50</math> miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging <math> 60</math> miles per hour. Leaving the car with her daughter, Bonnie rod a bus back to Austin along the same route and averaged <math> 40</math> miles per hour on the return trip. What was the average speed for the round trip, in miles per hour? | Austin and Temple are <math> 50</math> miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging <math> 60</math> miles per hour. Leaving the car with her daughter, Bonnie rod a bus back to Austin along the same route and averaged <math> 40</math> miles per hour on the return trip. What was the average speed for the round trip, in miles per hour? | ||
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<math> \textbf{(A)}\ 46 \qquad | <math> \textbf{(A)}\ 46 \qquad | ||
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\textbf{(D)}\ 52 \qquad | \textbf{(D)}\ 52 \qquad | ||
\textbf{(E)}\ 54</math> | \textbf{(E)}\ 54</math> | ||
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| + | ==Solution== | ||
| + | The way to Temple took <math>\frac{50}{60}=\frac56</math> hours, and the way back took <math>\frac{50}{40}=\frac54</math> for a total of <math>\frac56 + \frac54 = \frac{25}{12}</math> hours. The trip is <math>50\cdot2=100</math> miles. The average speed is <math>\frac{100}{25/12} = \boxed{\textbf{(B)}\ 48}</math> miles per hour. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=13|num-a=15}} | {{AMC8 box|year=2009|num-b=13|num-a=15}} | ||
Revision as of 16:01, 25 December 2012
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 rod 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.
See Also
| 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 | ||
