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

(Created page with "==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...")
 
m (Problem)
(10 intermediate revisions by 4 users not shown)
Line 1: Line 1:
 
==Problem==
 
==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?
+
It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How many seconds would it take Clea to ride the escalator down when she is not walking?
  
 +
<math>\textbf{(A)}\ 36\qquad\textbf{(B)}\ 40\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 52 </math>
  
 +
==Solution 1==
 +
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>
  
 +
==Solution 2==
 +
We write two equations using distance=rate * time. Let r be the rate she is walking, and e be the speed the escalator moves. WLOG, let the distance of the escalator be 120, as the distance is constant. Thus, our 2 equations are 120=60r and 120=24(r+e). Solving for e, we get e=3. Thus, it will take Clea 120/3 = <math>\boxed{\textbf{(B)}\ 40}</math> seconds
  
==Solution==
+
~coolmath2017
She walks at a rate of x units per second to travel a distance y. So 60x=y, and 24*(x+K)=y, where k is the speed of the escalator. so setting the two equations equal to each other, 60x=24x+24k, which means that 36x=24k; therefore, k=1.5x, so now divide 60 by 1.5 because you add the speed of the escalator but remove the walking, leaving the final answer that it takes 40 seconds to ride the escalator alone; answer choice B.
+
 
 +
== See Also ==
 +
 
 +
{{AMC12 box|year=2012|ab=B|num-b=8|num-a=10}}
 +
{{MAA Notice}}

Revision as of 18:25, 9 June 2020

Problem

It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How many 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 1

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 $\boxed{\textbf{(B)}\ 40}$

Solution 2

We write two equations using distance=rate * time. Let r be the rate she is walking, and e be the speed the escalator moves. WLOG, let the distance of the escalator be 120, as the distance is constant. Thus, our 2 equations are 120=60r and 120=24(r+e). Solving for e, we get e=3. Thus, it will take Clea 120/3 = $\boxed{\textbf{(B)}\ 40}$ seconds

~coolmath2017

See Also

2012 AMC 12B (ProblemsAnswer KeyResources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png