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Escalator Math
#854679
12/08/12 12:31 PM
12/08/12 12:31 PM
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Joined: Apr 2005
Posts: 37,822 Alabama
soot
OP
Puzzled Moderator
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OP
Puzzled Moderator
Sonic Boomer
Joined: Apr 2005
Posts: 37,822
Alabama
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When Ted walked down the down-moving escalator, he reached the bottom after taking 50 steps. As an experiment, he then ran up the same escalator, one step at a time, reaching the top after taking 125 steps. Assuming that Ted went up five times as fast as he went down (that is, took five steps to every one step before), and that he made each trip at a constant speed, how many steps would be visible if the escalator stopped running?
Last edited by soot; 12/09/12 11:48 AM.
Dan ... To learn, read...To know, write...To master, teach...To live, play games & listen to whale music Stay Smart & Stay Safe
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Re: Escalator Math
[Re: soot]
#854730
12/08/12 04:15 PM
12/08/12 04:15 PM
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Joined: Jan 2003
Posts: 5,763 Mojave desert, California
CCbomber
BAAG Specialist
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BAAG Specialist
Joined: Jan 2003
Posts: 5,763
Mojave desert, California
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I'm going out on a limb here.. D = # of steps showing when the escalator is stopped S = Ted's speed The ratio of the number of steps that passes a given point on the escalator when Ted is going up and down is proportional to Ted's speed going up and down. So, Ted going down D-50 S
---- = --
Ted going up D+125 5S
5D-250 = D+125 4D = 375 D = 93.75 steps
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Re: Escalator Math
[Re: Pandora]
#854781
12/08/12 10:06 PM
12/08/12 10:06 PM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
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I get 100...
d = distance (or number of visible steps) e = escalator speed (in steps per second)
Going down (assume a step takes 1 second): took 50 steps, so 50 seconds. So: d = 50 + 50e [1]
Going up (5 steps take 1 second (5 times faster)): took 125 steps @ 5 per second, so 25 seconds. So: d = 125 - 25e [2]
d = 50 + 50e [1] 2d=250 - 50e [2] * 2 ================ 3d = 300 d = 100
That gave me a headache...don't ask me to prove it!!
I'm a man of few words, BUT I use 'em often!!
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Re: Escalator Math
[Re: soot]
#854916
12/09/12 11:48 AM
12/09/12 11:48 AM
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Joined: Apr 2005
Posts: 37,822 Alabama
soot
OP
Puzzled Moderator
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OP
Puzzled Moderator
Sonic Boomer
Joined: Apr 2005
Posts: 37,822
Alabama
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Denis is correct...
One hundred steps.
Let n be the number of steps visible when the escalator is not moving, and let a unit of time be the time it takes Ted to walk down one step. If he walks down the down-moving escalator in 50 steps, then n - 50 steps have gone out of sight in 50 units of time. It takes him 125 steps to run up the same escalator, taking five steps to every one step before. In this trip, 125 - n steps have gone out of sight in 125/5, or 25 units of time. Since the escalator runs at a constant speed, we have the following linear equation that readily yields a value for n of 100 steps:
n-50 125 - n ____ = _______ 50 25
Dan ... To learn, read...To know, write...To master, teach...To live, play games & listen to whale music Stay Smart & Stay Safe
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