Difference between revisions of "2016 AMC 8 Problems/Problem 16"
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| + | ==Problem== | ||
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Annie and Bonnie are running laps around a <math>400</math>-meter oval track. They started together, but Annie has pulled ahead, because she runs <math>25\%</math> faster than Bonnie. How many laps will Annie have run when she first passes Bonnie? | Annie and Bonnie are running laps around a <math>400</math>-meter oval track. They started together, but Annie has pulled ahead, because she runs <math>25\%</math> faster than Bonnie. How many laps will Annie have run when she first passes Bonnie? | ||
<math>\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</math> | <math>\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</math> | ||
| − | ==Solution== | + | ==Solutions== |
| + | ===Solution 1=== | ||
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 <math>\boxed{\textbf{(D)}\ 5 }</math> laps. | 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 <math>\boxed{\textbf{(D)}\ 5 }</math> laps. | ||
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| − | ==Solution 2== | + | ===Solution 2=== |
| − | Call x the distance Annie runs. If Annie is 25% faster than Bonnie, then Bonnie will | + | Call <math>x</math> the distance Annie runs. If Annie is <math>25\%</math> faster than Bonnie, then Bonnie will run a distance of <math>\frac{4}{5}x</math>. For Annie to meet Bonnie, she must run an extra <math>400</math> meters, the length of the track. So <math>x-\left(\frac{4}{5}\right)x=400 \implies x=2000</math>, which is <math>\boxed{\textbf{(D)}\ 5 }</math> laps. |
- NoisedHens | - NoisedHens | ||
| − | + | ==Video Solution== | |
| + | https://youtu.be/lRbxzdBZpIY | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | {{AMC8 box|year=2016|num-b=15|num-a=17}} | ||
| + | {{MAA Notice}} | ||
Revision as of 15:32, 23 March 2022
Problem
Annie and Bonnie are running laps around a 
-meter oval track. They started together, but Annie has pulled ahead, because she runs 
faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
Solutions
Solution 1
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 
laps.
Solution 2
Call 
the distance Annie runs. If Annie is faster than Bonnie, then Bonnie will run a distance of 
. For Annie to meet Bonnie, she must run an extra meters, the length of the track. So 
, which is laps.
- NoisedHens
Video Solution
~savannahsolver
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
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| All AJHSME/AMC 8 Problems and Solutions | ||
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