2023 AMC 12A Problem 1

Problem 1 of 25EasierArithmetic

Cities

A

and

B

are

45

miles apart. Alicia lives in

A

and Beth lives in

B.

Alicia bikes towards

B

18

miles per hour. Leaving at the same time, Beth bikes toward

A

12

miles per hour. How many miles from City

A

will they be when they meet?

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Solution

The gap between them closes at

18+12=30

miles per hour, so they meet after

\dfrac{45}{30}=1.5

hours. In that time Alicia has ridden

18\cdot 1.5=27

miles from City

A.

Thus, the correct answer is E.

Tagged: distance rate and time