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| − | Cities <math>A</math> and <math>B</math> are <math>45</math> miles apart. Alicia lives in <math>A</math> and Beth lives in <math>B</math>. Alicia bikes towards <math>B</math> at 18 miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at 12 miles per hour. How many miles from City <math>A</math> will they be when they meet?
| + | #redirect[[2023 AMC 12A Problems/Problem 1]] |
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| − | <cmath>\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27</cmath>
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| − | ==Solution==
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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
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| − | == See Also ==
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| − | {{AMC10 box|year=2022|ab=B|before=First Problem|num-a=2}}
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| − | {{MAA Notice}}
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