Difference between revisions of "2023 AMC 10A Problems/Problem 1"
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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? | |
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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== | ||
+ | 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: | ||
+ | <cmath>12x+18x=45</cmath> | ||
+ | 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 |
Revision as of 14:39, 9 November 2023
Cities and are miles apart. Alicia lives in and Beth lives in . Alicia bikes towards at 18 miles per hour. Leaving at the same time, Beth bikes toward at 12 miles per hour. How many miles from City will they be when they meet?
Solution
This is a Distance=TimeSpeed so let be the time it takes to meet. We can write the following equation: Solving gives is . The is Alicia so
~zhenghua