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During AMC 10A/12A testing, the AoPS Wiki is in read-only mode and no edits can be made.

2007 AMC 12B Problems/Problem 2: Difference between revisions

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<math>\textbf{(A) } 22 \qquad\textbf{(B) } 24 \qquad\textbf{(C) } 25 \qquad\textbf{(D) } 26 \qquad\textbf{(E) } 28</math>
<math>\textbf{(A) } 22 \qquad\textbf{(B) } 24 \qquad\textbf{(C) } 25 \qquad\textbf{(D) } 26 \qquad\textbf{(E) } 28</math>


==Solution==
==Solution 1==
The trip was <math>240</math> miles long and took <math>\dfrac{120}{30}+\dfrac{120}{20}=4+6=10</math> gallons. Therefore, the average mileage was <math>\dfrac{240}{10}= \boxed{\mathrm{(B) \ } 24}</math>
The trip was <math>240</math> miles long and took <math>\dfrac{120}{30}+\dfrac{120}{20}=4+6=10</math> gallons. Therefore, the average mileage was <math>\dfrac{240}{10}= \boxed{\mathrm{(B) \ } 24}</math>
==Solution 2==
Alternatively, we can use the harmonic mean to get <math>\frac{2}{\frac{1}{20} + \frac{1}{30}} = \frac{2}{\frac{1}{12}} = 24</math> <math>\longrightarrow \boxed{(\textbf{B})}</math>


==See Also==
==See Also==

Revision as of 22:26, 12 January 2018

The following problem is from both the 2007 AMC 12B #2 and 2007 AMC 10B #3, so both problems redirect to this page.

Problem

A college student drove his compact car $120$ miles home for the weekend and averaged $30$ miles per gallon. On the return trip the student drove his parents' SUV and averaged only $20$ miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

$\textbf{(A) } 22 \qquad\textbf{(B) } 24 \qquad\textbf{(C) } 25 \qquad\textbf{(D) } 26 \qquad\textbf{(E) } 28$

Solution 1

The trip was $240$ miles long and took $\dfrac{120}{30}+\dfrac{120}{20}=4+6=10$ gallons. Therefore, the average mileage was $\dfrac{240}{10}= \boxed{\mathrm{(B) \ } 24}$

Solution 2

Alternatively, we can use the harmonic mean to get $\frac{2}{\frac{1}{20} + \frac{1}{30}} = \frac{2}{\frac{1}{12}} = 24$ $\longrightarrow \boxed{(\textbf{B})}$

See Also

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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 AMC 12 Problems and Solutions
2007 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
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 AMC 10 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

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