Number of Escalator Steps

  • Thread starter Pseudopro
  • Start date
In summary, we are given that person A takes 50 steps and person B takes 75 steps while the escalator is moving down. The time taken for person A to take one step is equal to the time taken for person B to take 3 steps. By assuming that the number of steps taken by A and B are sufficient for them to reach the bottom, we can deduce that they are going up a down moving escalator. Person B takes longer, so more steps have disappeared ahead of him. Person A takes 9/2 times as long, so 9m/2 steps have appeared ahead of him. In the end, person A takes a total of 75 + 9m/2 steps to reach the
  • #1
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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


??


The Attempt at a Solution


I think vm=3vc. ve=(se-75)/t etc. ... are we given enough information to complete the question?
 
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  • #2
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.
 
  • #3
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.
 

What is the definition of "Number of Escalator Steps"?

The number of escalator steps refers to the total number of individual steps that make up an escalator, including both the upward and downward sections.

How is the number of escalator steps determined?

The number of escalator steps is determined by the length and height of the escalator, as well as the desired speed and step size. It is typically calculated by engineers during the design and construction process.

What is the average number of escalator steps in a standard escalator?

The average number of escalator steps in a standard escalator is typically between 24 and 28 steps for a height of 12-14 feet. However, this can vary depending on the manufacturer and specific design of the escalator.

Can the number of escalator steps be changed or adjusted?

Yes, the number of escalator steps can be changed or adjusted during the installation process or even after installation. However, this would require significant modifications to the escalator and is not a common practice.

What safety precautions are taken in regards to the number of escalator steps?

The number of escalator steps is carefully calculated to ensure the safety of users. The steps are typically evenly spaced and have a non-slip surface to prevent accidents. Additionally, sensors and other safety features are installed to detect and prevent any issues with the escalator steps.

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