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 times as fast as Bella walks. The distance between their houses is miles, which is feet, and Bella covers feet with each step. How many steps will Bella take by the time she meets Ella?
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Solution:
By the time that the two girls meet, Ella will ride times the distance that Bella walks, so Ella will ride of the total= distance, and Bella will walk of the total distance, or feet. Each of her steps covers = feet, so the number of steps she will take is = .
Bella's rate is feet per step whereas Ella travels feet for each of Bella's steps. So together they travel 15 feet for each of Bella's steps. Hence the number of steps taken by Bella when she meets Ella is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions