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Difference between revisions of "2012 AMC 12B Problems/Problem 9"

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==Solution==
 
==Solution==
 
She walks at a rate of <math>x</math> units per second to travel a distance <math>y</math>. As <math>vt=d</math>, we find <math>60x=y</math> and <math>24*(x+k)=y</math>, where <math>k</math> is the speed of the escalator. Setting the two equations equal to each other, <math>60x=24x+24k</math>, which means that <math>k=1.5x</math>. Now we divide <math>60</math> by <math>1.5</math> because you add the speed of the escalator but remove the walking, leaving the final answer that it takes to ride the escalator alone as <math>\boxed{\textbf{(B)}\ 40}</math>
 
She walks at a rate of <math>x</math> units per second to travel a distance <math>y</math>. As <math>vt=d</math>, we find <math>60x=y</math> and <math>24*(x+k)=y</math>, where <math>k</math> is the speed of the escalator. Setting the two equations equal to each other, <math>60x=24x+24k</math>, which means that <math>k=1.5x</math>. Now we divide <math>60</math> by <math>1.5</math> because you add the speed of the escalator but remove the walking, leaving the final answer that it takes to ride the escalator alone as <math>\boxed{\textbf{(B)}\ 40}</math>
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== See Also ==
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{{AMC12 box|year=2012|ab=B|num-b=8|num-a=10}}

Revision as of 22:19, 12 January 2013

Problem

It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How seconds would it take Clea to ride the escalator down when she is not walking?

$\textbf{(A)}\ 36\qquad\textbf{(B)}\ 40\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 52$

Solution

She walks at a rate of $x$ units per second to travel a distance $y$. As $vt=d$, we find $60x=y$ and $24*(x+k)=y$, where $k$ is the speed of the escalator. Setting the two equations equal to each other, $60x=24x+24k$, which means that $k=1.5x$. Now we divide $60$ by $1.5$ because you add the speed of the escalator but remove the walking, leaving the final answer that it takes to ride the escalator alone as $\boxed{\textbf{(B)}\ 40}$

See Also

2012 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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 AMC 12 Problems and Solutions
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