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Difference between revisions of "2018 AMC 8 Problems/Problem 17"

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==Solution==
 
==Solution==
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Since Ella rides 5 times as fast as Bella, Ella rides at a rate of <math>\frac{25}{2}</math> or <math>12 \tfrac{1}{2}</math>. Together, they move <math>15</math> feet towards each other every unit. You divide <math>10560</math> by <math>15</math> to find the number of steps Ella takes, which results in the answer of <math>704</math> or <math>\textbf{(A) }</math>
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Since Ella rides 5 times as fast as Bella, Ella rides at a rate of <math>\frac{25}{2}</math> or <math>12 \tfrac{1}{2}</math>. Together, they move <math>15</math> feet towards each other every unit. You divide <math>10560</math> by <math>15</math> to find the number of steps Ella takes, which results in the answer of <math>\boxed{\textbf{(A) }704}</math>
  
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==See Also==
 
{{AMC8 box|year=2018|num-b=16|num-a=18}}
 
{{AMC8 box|year=2018|num-b=16|num-a=18}}
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{{MAA Notice}}

Revision as of 18:25, 21 November 2018

Problem 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 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

Since Ella rides 5 times as fast as Bella, Ella rides at a rate of $\frac{25}{2}$ or $12 \tfrac{1}{2}$. Together, they move $15$ feet towards each other every unit. You divide $10560$ by $15$ to find the number of steps Ella takes, which results in the answer of $\boxed{\textbf{(A) }704}$

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

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