Difference between revisions of "2012 AMC 12B Problems/Problem 9"
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| − | She walks at a rate of x units per second to travel a distance y. | + | She walks at a rate of <math>x</math> units per second to travel a distance <math>y</math>. As <math>vt=d</math>, <math>60x=y</math>, and <math>24*(x+k)=y</math>, where <math>k</math> is the speed of the escalator. so setting the two equations equal to each other, <math>60x=24x+24k</math>, which means that <math>k=1.5x</math>. Now we divide <math>60</math> by <math>1.5</math> 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 <math>\boxed{\textbf{(B)}\ 40}</math> |
Revision as of 01:29, 9 March 2012
Problem
It takes Clea 60 seconds to walk down an escalator when it is not moving, and 24 seconds when it is moving. How seconds would it take Clea to ride the escalator down when she is not walking?
Solution
She walks at a rate of 
units per second to travel a distance 
. As 
, 
, and 
, where 
is the speed of the escalator. so 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 
