Difference between revisions of "2007 AMC 12B Problems/Problem 2"

m
 
(5 intermediate revisions by 3 users not shown)
Line 2: Line 2:
  
 
==Problem==
 
==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?
 
  
<math>\mathrm {(A)} 22</math>  <math>\mathrm {(B)} 24</math>  <math>\mathrm {(C)} 25</math>   <math>\mathrm {(D)} 26</math>   <math>\mathrm {(E)} 28</math>
+
A college student drove his compact car <math>120</math> miles home for the weekend and averaged <math>30</math> miles per gallon. On the return trip the student drove his parents' SUV and averaged only <math>20</math> miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?
  
==Solution==
+
<math>\textbf{(A) } 22 \qquad\textbf{(B) } 24 \qquad\textbf{(C) } 25 \qquad\textbf{(D) } 26 \qquad\textbf{(E) } 28</math>
The trip was 240 milesand <math>\dfrac{120}{30}+\dfrac{120}{20}=4+6=10</math> gallons. Therefore, the average milage was <math>\dfrac{240}{10}=24 \Rightarrow \mathrm {(B)}</math> miles per gallon.
+
 
 +
==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{\textbf{(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}} = \boxed{\textbf{(B) }24}</math>
  
 
==See Also==
 
==See Also==
  
 
{{AMC12 box|year=2007|ab=B|num-b=1|num-a=3}}
 
{{AMC12 box|year=2007|ab=B|num-b=1|num-a=3}}
 +
 +
{{AMC10 box|year=2007|ab=B|num-b=2|num-a=4}}
 +
{{MAA Notice}}

Latest revision as of 10:49, 7 March 2022

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 $\dfrac{240}{10}= \boxed{\textbf{(B) }24}$

Solution 2

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

See Also

2007 AMC 12B (ProblemsAnswer KeyResources)
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 (ProblemsAnswer KeyResources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png