2012 AMC 10B Problems/Problem 13
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 1
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.
Solution 2
Let be the speed of the escalator and be the speed of Clea. Then without loss of generality, assume that the length of the escalator be 1. Then and , so . Thus the time it takes for Clea to ride down the operating escalator when she just stands on it is .
Solution 3
WLOG, let the length of the escalator be ft. So, Clea's rate is feet per second (fps), and the escalator and Clea's rate is fps. So, the escalator's rate is fps. Therefore, .
not to be confused with frames per second.
~MrThinker
Video Solution
~savannahsolver
See Also.
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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