Difference between revisions of "2022 AMC 10A Problems/Problem 2"

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<math>\textbf{(A) } 5 \qquad\textbf{(B) } 7 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 13</math>
 
<math>\textbf{(A) } 5 \qquad\textbf{(B) } 7 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 13</math>
  
== Solution ==  
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== Solution 1==  
  
 
Mike's speed is <math>\frac{15}{57}=\frac{5}{19}</math> laps per minute.
 
Mike's speed is <math>\frac{15}{57}=\frac{5}{19}</math> laps per minute.
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~MRENTHUSIASM
 
~MRENTHUSIASM
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== Solution 2==
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Mike runs <math>1</math> lap in <math>\frac{57}{15}=\frac{19}{5}</math> minutes. So, in <math>27</math> minutes, Mike ran about <math>\frac{27}{\frac{19}{5}} \approx \boxed{\textbf{(B) }7}</math> laps.
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~MrThinker
  
 
==Video Solution 1 (Quick and Easy)==
 
==Video Solution 1 (Quick and Easy)==

Revision as of 15:39, 14 November 2022

Problem

Mike cycled $15$ laps in $57$ minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first $27$ minutes?

$\textbf{(A) } 5 \qquad\textbf{(B) } 7 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 13$

Solution 1

Mike's speed is $\frac{15}{57}=\frac{5}{19}$ laps per minute.

In the first $27$ minutes, he completed approximately $\frac{5}{19}\cdot27\approx\frac{1}{4}\cdot28=\boxed{\textbf{(B) } 7}$ laps.

~MRENTHUSIASM

Solution 2

Mike runs $1$ lap in $\frac{57}{15}=\frac{19}{5}$ minutes. So, in $27$ minutes, Mike ran about $\frac{27}{\frac{19}{5}} \approx \boxed{\textbf{(B) }7}$ laps.

~MrThinker

Video Solution 1 (Quick and Easy)

https://youtu.be/tu4rE1nqY9g

~Education, the Study of Everything

See Also

2022 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AMC 10 Problems and Solutions

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