Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

m
m
 
(8 intermediate revisions by 6 users not shown)
Line 1: Line 1:
−
2. 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?
+
{{duplicate|[[2007 AMC 12B Problems|2007 AMC 12B #2]] and [[2007 AMC 10B Problems|2007 AMC 10B #3]]}}
  
−
A. 22 B. 24 C. 25 D. 26 E. 28
+
==Problem==
  
 +
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?
  
−
{{wikify}}
+
<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{\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==
 +
 
 +
{{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 09:49, 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 (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

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_AMC_12B_Problems/Problem_2&oldid=172425"