2023 AMC 10A Problems/Problem 1

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

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

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2023 AMC 10A Problems/Problem 1

Solution