Difference between revisions of "2012 AMC 10B Problems/Problem 13"
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| + | == Problem == | ||
| + | It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it? | ||
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| + | <math> \textbf{(A)}\ 36\qquad\textbf{(B)}\ 40\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 52 </math> | ||
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== Solution == | == Solution == | ||
Revision as of 20:18, 8 February 2014
Problem
It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?
Solution
Let 
be the speed of the escalator and 
be the speed of Clea. Using 
, the first statement can be translated to the equation 
. The second statement can be translated to 
. Since the same distance is being covered in each scenario, we can set the two equations equal and solve for . We find that 
. The problem asks for the time it takes her to ride down the escalator when she just stands on it. Since 
and , we have 
seconds. Answer choice 
is correct.
See Also
| 2012 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
