Difference between revisions of "2012 AMC 12B Problems/Problem 9"
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− | Clea covers <math>\dfrac{1}{60}</math> of the escalator every second. Say the escalator covers <math>\dfrac{1}{r}</math> of the escalator every second. Since Clea and the escalator cover the entire escalator in <math>24</math> seconds, we can use distance <math>=</math> rate <math>\cdot</math> time to get <math>24\left(\dfrac{1}{60} + \dfrac{1}{r}\right) = 1</math>. Solving gives us <math>r = 40</math>, so if Clea were to just stand on the escalator, it would take her <math>\boxed{\textbf{(B)}\ 40}</math> seconds to get down. | + | Clea covers <math>\dfrac{1}{60}</math> of the escalator every second. Say the escalator covers <math>\dfrac{1}{r}</math> of the escalator every second. Since Clea and the escalator cover the entire escalator in <math>24</math> seconds, we can use distance <math>=</math> rate <math>\cdot</math> time to get <math>24\left(\dfrac{1}{60} + \dfrac{1}{r}\right) = 1</math>. Solving gives us <math>r = 40</math>, so if Clea were to just stand on the escalator, it would take her <math>\boxed{\textbf{(B)}\ 40}</math> seconds to get down. ~Extremelysupercooldude |
== See Also == | == See Also == |
Latest revision as of 07:14, 29 June 2023
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[hide]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?
Solution 1
She walks at a rate of units per second to travel a distance . As , we find and , where is the speed of the escalator. Setting the two equations equal to each other, , which means that . Now we divide by 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
Solution 2
We write two equations using distance = rate * time. Let be the rate she is walking, and be the speed the escalator moves. WLOG, let the distance of the escalator be , as the distance is constant. Thus, our equations are and . Solving for , we get . Thus, it will take Clea seconds.
~coolmath2017 ~Extremelysupercooldude (Latex edits)
Solution 3
Clea covers of the escalator every second. Say the escalator covers of the escalator every second. Since Clea and the escalator cover the entire escalator in seconds, we can use distance rate time to get . Solving gives us , so if Clea were to just stand on the escalator, it would take her seconds to get down. ~Extremelysupercooldude
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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