Difference between revisions of "2023 AMC 12A Problems/Problem 1"

(Solution 1)
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==Solution 1==
 
==Solution 1==
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This is a Distance=Time<math>\times</math>Speed so let <math>x</math> be the time it takes to meet. We can write the following equation:
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<cmath>12x+18x=45</cmath>
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Solving gives is <math>x=1.5</math>. The <math>18x</math> is Alicia so <math>18\times1.5=\boxed{\text{(E) 27}}</math>
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~zhenghua
  
 
==See also==
 
==See also==

Revision as of 16:03, 9 November 2023

Problem

Cities $A$ and $B$ are $45$ miles apart. Alicia lives in $A$ and Beth lives in $B$. Alicia bikes towards $B$ at 18 miles per hour. Leaving at the same time, Beth bikes toward $A$ at 12 miles per hour. How many miles from City $A$ will they be when they meet? $\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27$

Solution 1

This is a Distance=Time$\times$Speed so let $x$ be the time it takes to meet. We can write the following equation: \[12x+18x=45\] Solving gives is $x=1.5$. The $18x$ is Alicia so $18\times1.5=\boxed{\text{(E) 27}}$

~zhenghua

See also

2023 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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
2023 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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

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