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 15:39, 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