Ludy Aquino Skinned The Cat Another Way

As promised, we print below Ludy's solution to the Escalator Puzzle after he expounded on his steps and notations. No, he did not take an extended time to solve it. I am simply late in posting it because i have also a job to attend to first hehehe... Now, you can dare to compare with that of Carlo...

The Office Escalator
It’s 3 o’clock in the afternoon and everyone was in a hurry to get home. Our Managing Director was generous enough to let everyone go early for the day, giving them time to prepare for New Year’s Eve. So I hurriedly shuffled the loose pile of paper on my desk and pushed each one into the trays, shut down my laptop and shoved it into its carrying case. “Happy New Year. See you next year, everyone”, I hollered to nobody in particular as I walked to the exits. Work could wait for next year which will start next Sunday! Everyone was filing out of the office into the parking lot. I needed to go, too! I could not wait for the slow descent of the escalator so I walked down even as it descended. It took me 10 steps with my normal gait to get down from the First Floor level to the Ground Floor level. I was about to dash away to the Parking Exits when Mar, looking down from the Second Floor level called my attention. “Hey, Sonny – you dropped your wallet.” In my eagerness, I dropped my wallet at the top of the descending flight that I just traversed. Wanting to get to my wallet as quickly as possible, I forgot to use the ascending flight and instead huff-and-puff my way up the descending flight at a rate which is 5 times my pace in going down. It took me 25 steps before I got to my wallet – thank God. Now Louisian Engineers, pray tell me how many steps has our office escalator?

Ludy's Solution:
Let
W = my walking rate in going down (steps/sec)
V = rate of escalator’s descent (steps/sec)
t = time it took me to go down in seconds
u = time it took me to go up in seconds

S = the number of steps between floors

In going down, the rate of descent will be the sum of my walking rate and the escalator’s rate of descent or (W + V). The total number of steps, S will be covered in time, t and therefore:

S = (W + V) x t

On the same duration, I made 10 steps which means

W x t = 10 or my walking rate,W = 10/t

In going up, I increased my rate 5 fold to go against the downward rate of the escalator so that my net rate of ascent is (5W – V). Thus, to cover the entire flight of escalator, u seconds would be needed, therefore:

S = (5W – V) x u

On the same duration, I made 25 steps which means

5W x u = 25 or W = 5/u

Therefore: 10/t = 5/u; and further: u = t/2

Now, the number of steps between floors should be the same whether going up or going down, therefore:

(W + V) x t = (5W – V) x u
(W + V) x t = (5W – V) x t/2

Which simplifies to

W = V (walking rate is equal to the escalator’s descent rate)

which means that if I covered 10 steps in going down, the escalator also descended by the same number of steps. Together, we covered a total of 20 steps.

Therefore, there are twenty steps between the floors!

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Who could question such flawless and compelling logic? There you go, my dear Louisians. We could only read and ponder in awe... hehehe. Anymore questions, class?

ise

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