A man walks up an escalator, taking one step per second. After taking thirty steps, he is at the top.
Next day, he goes up at two steps per second, reaching the top in 36 steps.
The third day, he has had a long afternoon and merely sits on the escalator, waiting for it to reach the top.
How long does it take him?
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Submitted by DJ
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Rating: 4.2632 (19 votes)
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Solution:
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1½ minutes
Let s=the number of steps to the top of the escalator (when it is not moving), and r=the rate of the escalator in steps per second.
Use the equivalent equations:
distance=rate*time
time=distance/rate
First, each day, the time it took him to go up is the number of steps he took, divided by the number of steps he took each second.
So the first day, it took him 30/1=30 seconds to reach the top, and the second day, it took him 36/2=18 seconds to reach the top.
Also for each day, the distance the escalator travels while he is on it is the total number of steps from top to bottom, minus the number of steps he took. The rate of the escalator is constant, and the time it took the man to walk up is determined by the relationship above:
The first day: s-30 = 30r
and
The second day: s-36 = 18r.
Solving this system of equations yields s=45 and r=.5, or there are 45 steps from the bottom to the top of the escalator, moving upwards at a rate of one step every two seconds.
If Alan just sits and waits for the escalator, will take him 45/.5 = 90 seconds, or a minute and a half, to reach the top. |
