2023 AMC 10A Problem 1

Below is the professionally curated solution for Problem 1 of the 2023 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 10A solutions, or check the answer key.

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Concepts:relative speed distance rate and time

Difficulty rating: 890

Cities $A$ and $B$ are $45$ miles apart. Alice and Beth start biking from $A$ and $B$ at speeds of $18$ mph and $12$ mph, respectively. How far away from city $A$ will they be when they meet?

$20$

$24$

$25$

$26$

$27$

Solution:

They ride toward each other, so their speeds add. That closes the $45$ -mile gap at $18 + 12 = 30$ mph, and they meet after $45/30 = 1.5$ hours. Alice starts at $A,$ so by then she's gone $18 \cdot 1.5 = 27$ miles. Thus, E is the correct answer.

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