2018 AMC 8 Problems/Problem 17
Contents
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?
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 the times for both girls must be the same, and so that means in d/5r = t, the numerator 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 10,560 feet is 1,760 feet. Bella also walks 2.5 feet each step, and 1,760 divided by 2.5 is 
.
Solution 2 (Use Answer Choices to our advantage)
We know that Bella goes 2.5 feet per step and since Ella rides 5 times faster than Bella she must go 12.5 feet on her bike for every step of Bella's. For Bella, it takes 4,224 steps, and for Ella, it takes 1/5th those steps since Ella goes 5 times faster than Bella, taking her 844.8 steps. The number of steps where they meet therefore must be less than 844.8. The only answer choice less than it is .
Video Solution
~savannahsolver
https://www.youtube.com/watch?v=UczCIsRzAeo
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
