2018 AMC 8 Problems/Problem 17

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 5 times as fast as Bella walks. The distance between their houses is $2$ miles, which is $10,560$ feet, and Bella covers $2 \tfrac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella?

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

Solution 1

Since Ella rides 5 times faster than Bella, the ratio of their speeds is 5:1. For Bella, we have D/R = t and for Ella, we have D/5r = t, however we know times for both girls must be the same, and so that means in D/5R = t, numertator becomes 5D(Ella travels 5 times the distance that Bella does). This means that Bella travels 1/6 of the way, and 1/6 of 10560 feet is 1760 feet. Bella also walks 2.5 feet in a step, and 1760 divided by 2.5 is $\boxed{\textbf{(A) }704}$ .

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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All AJHSME/AMC 8 Problems and Solutions

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2018 AMC 8 Problems/Problem 17

Problem

Solution 1

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