2016 AMC 8 Problems/Problem 16

Revision as of 18:56, 12 November 2019 by Jackshi2006 (talk | contribs) (Solution 2)

Annie and Bonnie are running laps around a $400$-meter oval track. They started together, but Annie has pulled ahead, because she runs $25\%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?

$\textbf{(A) }1\dfrac{1}{4}\qquad\textbf{(B) }3\dfrac{1}{3}\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad \textbf{(E) }25$

Solution

Each lap Bonnie runs, Annie runs another quarter lap, so Bonnie will run four laps before she is overtaken. This means that Annie and Bonnie are equal so that Annie needs to run another lap to overtake Bonnie. That means Annie will have run $\boxed{\textbf{(D)}\ 5 }$ laps.

2016 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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Solution 2

Call x the distance Annie runs. If Annie is 25% faster than Bonnie, then Bonnie will be 4/5x. For Annie to meet Bonnie, she must run an extra 400 meters, the length of the track. So x-(\[\frac{4}{5}\])x=400. You get 1/5x=400, or x=2000, which is $\boxed{\textbf{(D)}\ 5 }$ laps.

- NoisedHens

Someone, please help with the latex. I also don't know why this solution is moved to the bottom of the page. Delete these two lines when the issues have been resolved.

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