Difference between revisions of "2025 AMC 8 Problems/Problem 19"

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The 2025 AMC 8 is not held yet. Please do not post false problems.
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Two towns, <math>A</math> and <math>B</math>, are connected by a straight road, <math>15</math> miles long. Traveling from town <math>A</math> to town <math>B</math>, the speed limit changes every <math>5</math> miles: from <math>25</math> to <math>40</math> to <math>20</math> miles per hour (mph). Two cars, one at town <math>A</math> and one at town <math>B</math>, start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town <math>A</math>, in miles, will the two cars meet?
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<math>\textbf{(A)}\ 7.75\qquad \textbf{(B)}\ 8\qquad \textbf{(C)}\ 8.25\qquad \textbf{(D)}\ 8.5\qquad \textbf{(E)}\ 8.75</math>

Revision as of 22:02, 29 January 2025

Two towns, $A$ and $B$, are connected by a straight road, $15$ miles long. Traveling from town $A$ to town $B$, the speed limit changes every $5$ miles: from $25$ to $40$ to $20$ miles per hour (mph). Two cars, one at town $A$ and one at town $B$, start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town $A$, in miles, will the two cars meet?

$\textbf{(A)}\ 7.75\qquad \textbf{(B)}\ 8\qquad \textbf{(C)}\ 8.25\qquad \textbf{(D)}\ 8.5\qquad \textbf{(E)}\ 8.75$