2009 AMC 8 Problems/Problem 14: Difference between revisions
MRENTHUSIASM (talk | contribs) Undo revision 160263 by Raina0708 (talk) LaTeX makes the solution look neat and professional. I PM'ed Raina0708 and asked the user NOT to remove the LaTeX. I will undo this change. Tag: Undo |
|||
| Line 10: | Line 10: | ||
==Solution== | ==Solution== | ||
The way to Temple took 50 | 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. | ||
==Solution 2== | ==Solution 2== | ||
Revision as of 15:32, 14 August 2021
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
This question simply asks for the harmonic mean of and , regardless of how far Austin and Temple are.
Plugging in, we have: 
miles per hour.
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination
