Escalator Steps and Time: Solving for Stationary Step Count

[Pseudopro]

Homework Statement

An escalator is moving down. Person A takes 50 steps and Person B takes 75 steps while it is moving down. The time taken by Person A to take one step is equal to the time taken by Person B to take 3 steps. Find the number of steps in the escalator while it is stationary.

Homework Equations

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The Attempt at a Solution

I think v_m=3v_c. v_e=(s_e-75)/t etc. ... are we given enough information to complete the question?

 

[HallsofIvy]

Well, in order to be able to do this, we must assume that the number of steps A and B each take, together with the motion of the elevator, are sufficient for them to get to the bottom. Call the time it takes person A to take one step, T, and the number of steps in the entire escalator, n. Person A takes time 50T altogether while person B takes time 75(3T)=225T. The first thing that tells me is that I am thinking about this wrong! If person B is takes longer then more steps of the escalator have disappeared ahead of him and so he should take fewer steps not more. It appears that A and B are going up a down moving escalator- a singularly silly exercise.

If m steps have appeared ahead of B while he was moving, he went a total of 75+m steps. A took (75/50)*3= 9/2 times as long and so 9m/2 steps appeared ahead of him. He took a total of 75+ 9m/2 steps to get to the top.

 

[verty]

It does seem contradictory that B takes more steps but walks faster. That's just the nature of escalators. The escalator has less time to carry B to the bottom because B is determined to make it a personal effort. So less steps have disappeared for him, and he walks farther on his own. And we know how much longer he took, this is the key piece of information.