Question

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?

$20$

$24$

$25$

$26$

$27$

Answer: E

Concepts:relative speed distance rate and time

Difficulty rating: 890

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.

2023 AMC 10A Problem 1

Answer: E

Difficulty rating: 890

Solution:

Problem 1 in Other Years