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2023 AMC 10A 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

They ride toward each other, so their speeds add. That closes the 4545-mile gap at 18+12=3018 + 12 = 30 mph, and they meet after 4530=1.5\frac{45}{30} = 1.5 hours. Alice starts at A,A, so by then she’s gone 181.5=2718 \cdot 1.5 = 27 miles. Thus, E is the correct answer.

More practice

Concepts: relative speed · distance rate and time

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