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

Revision as of 06:58, 29 June 2023

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 $\dfrac{120}{3} = \boxed{\textbf{(B)}\ 40}$ seconds.

~coolmath2017 ~Extremelysupercooldude (Latex edits)

Solution 3

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

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

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 ~coolmath2017
 ~Extremelysupercooldude (Latex edits)
+==Solution 3==
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