Difference between revisions of "2017 AMC 10B Problems/Problem 2"

(Video Solution (HOW TO CRITICALLY THINK!!!))
 
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If Sofia ran the first <math>100</math> meters of each lap at <math>4</math> meters per second and the remaining <math>300</math> meters of each lap at <math>5</math> meters per second, then she took <math>\frac{100}{4}+\frac{300}{5}=25+60=85</math> seconds for each lap. Because she ran <math>5</math> laps, she took a total of <math>5 \cdot 85=425</math> seconds, or <math>7</math> minutes and <math>5</math> seconds. The answer is <math>\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}</math>.
 
If Sofia ran the first <math>100</math> meters of each lap at <math>4</math> meters per second and the remaining <math>300</math> meters of each lap at <math>5</math> meters per second, then she took <math>\frac{100}{4}+\frac{300}{5}=25+60=85</math> seconds for each lap. Because she ran <math>5</math> laps, she took a total of <math>5 \cdot 85=425</math> seconds, or <math>7</math> minutes and <math>5</math> seconds. The answer is <math>\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}</math>.
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==Video Solution (HOW TO CRITICALLY THINK!!!)==
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https://youtu.be/RAXT96AO9kQ
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~Education, the Study of Everything
  
 
==Video Solution==
 
==Video Solution==
 
https://youtu.be/TazCyhFgINI
 
https://youtu.be/TazCyhFgINI
  
~savannahsolver
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==Video Solution ==
 
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https://youtu.be/zTGuz6EoBWY?t=275
==Video Solution by the Beauty of Math / icematrix==
 
With whiteboard at home: https://www.youtube.com/watch?v=zTGuz6EoBWY
 
 
 
~IceMatrix
 
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2017|ab=B|num-b=1|num-a=3}}
 
{{AMC10 box|year=2017|ab=B|num-b=1|num-a=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 13:57, 6 June 2023

Problem

Sofia ran $5$ laps around the $400$-meter track at her school. For each lap, she ran the first $100$ meters at an average speed of $4$ meters per second and the remaining $300$ meters at an average speed of $5$ meters per second. How much time did Sofia take running the $5$ laps?

$\qquad\textbf{(A)}\ \text{5 minutes and 35 seconds}$
$\qquad\textbf{(B)}\ \text{6 minutes and 40 seconds}$
$\qquad\textbf{(C)}\ \text{7 minutes and 5 seconds}$
$\qquad\textbf{(D)}\ \text{7 minutes and 25 seconds}$
$\qquad\textbf{(E)}\ \text{8 minutes and 10 seconds}$

Solution

If Sofia ran the first $100$ meters of each lap at $4$ meters per second and the remaining $300$ meters of each lap at $5$ meters per second, then she took $\frac{100}{4}+\frac{300}{5}=25+60=85$ seconds for each lap. Because she ran $5$ laps, she took a total of $5 \cdot 85=425$ seconds, or $7$ minutes and $5$ seconds. The answer is $\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}$.

Video Solution (HOW TO CRITICALLY THINK!!!)

https://youtu.be/RAXT96AO9kQ

~Education, the Study of Everything

Video Solution

https://youtu.be/TazCyhFgINI

Video Solution

https://youtu.be/zTGuz6EoBWY?t=275

See Also

2017 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AMC 10 Problems and Solutions

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