Difference between revisions of "2012 AMC 12B Problems/Problem 9"
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==Solution 3== | ==Solution 3== | ||
| − | 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 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
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
