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April 2, 2009

Escalator Puzzles



There is an Escalator and 2 persons move down it.A takes 50 steps
and B takes 75 steps while the escalator is moving down.
Given that the time taken by A to take 1 step is equal to time taken
by B to take 3 steps. Find the no. of steps in the escalator
while it is stationary ?

7 comments:

Secret Squïrrel said...

In the time B takes to pass 75 steps, A covers only 25. When B reaches the bottom of the escalator A will be halfway down (25 is half 50).

If the escalator were stationary, B would travel 3 times as fast as A, but B is only twice as fast as A (because the escalator contributes equally to both of their speeds).

Therefore,
B+E = 2(A+E).
Since we know that B = 3A:
3A+E = 2A+2E
A = E

So, assuming constant velocity, the escalator's speed must be the same as A's and in the time it takes A to traverse its length (50 steps), another 50 will have passed under the floor.

The escalator has 100 steps.

Anonymous said...

I want to say that's what was meant by this but it actually asks
"Find the no. of steps in the escalator while it is stationary?"

And it clearly says "the escalator is moving down"

now if the question was
"Find the no. of steps in the escalator IF it is stationary?"
you'd be right.

Meaning the real answer is 0.
:3

Anonymous said...

I want to say that's what was meant by this but it actually asks
"Find the no. of steps in the escalator while it is stationary?"

And it clearly says "the escalator is moving down"

now if the question was
"Find the no. of steps in the escalator IF it is stationary?"
you'd be right.

Meaning the real answer is 0.
:3

Secret Squïrrel said...

It could be clearer but I think the answer that is sought is the number of steps that are visible. Whether it is stationary or not makes no difference - you could take a photo if it were moving and the answer would be the same (assuming that the Lorentz contraction can be ignored ;-)

Anonymous said...

Tell the answer!

Anonymous said...

Dear Mr. Squrell,
There's a major flaw in the soln. offered by u.
as when u say
B + E = 2( A + E) u already have presumed that A =E n so there's no merit in arriving at it. it'd b very nice of u in explaining the bedrocks involved in.
thnx in anticipation,
god bless

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