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2023 AMC 10A Problem 1

Problem 1 of 25EasierArithmetic

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 18⋅1.5=2718 \cdot 1.5 = 27 miles. Thus, E is the correct answer.
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Tagged: relative speed · distance rate and time

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