2018 AMC 8 Problem 17

Below is the video solution and professionally curated solution for Problem 17 of the 2018 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 8 solutions, or check the answer key.

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Concepts:distance rate and timeratio and proportionunit conversion

Difficulty rating: 1210

17.

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 \tfrac{1}{2} feet with each step. How many steps will Bella take by the time she meets Ella?

704 704

845 845

1056 1056

1760 1760

3520 3520

Video solution:
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Written solution:

Since for every foot Bella walks, Ella rides 5 feet, we know that Bella will walk 16\frac16 of the distance between the two houses, and so she walks 1610560=1760\dfrac16 \cdot 10560=1760 feet. Since she walks 2.52.5 feet per step, she takes 17602.5=704\dfrac{1760}{2.5} = 704 steps by the time she meets Ella.

Thus, A is the correct answer.

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