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Problem 17 (2018 AMC 8)

AMC 8Medium

From module Kinematics and Rates

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Understand the scale
Scale 0.5: Easiest math competition problems, often solvable even for early middle school students without experience. 1: Problems strictly for beginners, often at a moderate middle school level. 1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests. 2: For motivated beginners, harder questions from the previous categories. 2.5: More advanced beginner problems, hardest questions from previous categories. 3: Early intermediate problems that require more creative thinking. 3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge. 4: Intermediate-level problems. 4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions. 5: More difficult AIME problems or simple proof-based Olympiad-style problems. 6: High-level AIME-styled questions or introductory Olympiad-level questions. 7: Tougher Olympiad-level questions, may require more technical knowledge. 8: High-level Olympiad-level questions. 9: Expert Olympiad-level questions. 9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve. 10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
RatesDistance Speed TimeRatios

Problem

Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 55 times as fast as Bella walks. The distance between their houses is 22 miles, which is 10,56010{,}560 feet, and Bella covers 2122\frac{1}{2} feet with each step. How many steps will Bella take by the time she meets Ella?

(A) 704(B) 845(C) 1056(D) 1760(E) 3520\textbf{(A)}\ 704 \qquad \textbf{(B)}\ 845 \qquad \textbf{(C)}\ 1056 \qquad \textbf{(D)}\ 1760 \qquad \textbf{(E)}\ 3520

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