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2023 AMC 12A Problem 1

Problem 1 of 25EasierAlgebra

Cities AA and BB are 4545 miles apart. Alicia lives in AA and Beth lives in B.B. Alicia bikes towards BB at 1818 miles per hour. Leaving at the same time, Beth bikes toward AA at 1212 miles per hour. How many miles from City AA will they be when they meet?

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Solution

The gap between them closes at 18+12=3018+12=30 miles per hour, so they meet after 4530=1.5\dfrac{45}{30}=1.5 hours. In that time Alicia has ridden 18⋅1.5=2718\cdot 1.5=27 miles from City A.A. Thus, the correct answer is E.

More practice

Concepts: distance rate and time

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.