# Number of Steps on a Stationary Escalator with Varying Person Speeds

• tomas krchnak
In summary, the conversation is about finding the number of steps on an escalator while it is stationary. A and B take 50 and 75 steps respectively while the escalator is moving. The time taken for A to take 1 step is equal to the time taken for B to take 3 steps. By setting up a system of equations, it is determined that the number of steps on the escalator is 100, and therefore, 50 steps can be seen while it is stationary.
tomas krchnak

## Homework Statement

There is a escalator and 2 persons move up it. A takes 50 steps and B takes 75 steps while the escalator is moving up. 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 that is possible to see while it is staionary.?

## The Attempt at a Solution

v is the speed of persons (A=1v, B=3v)
x is the number of stairs
y is the speed of escalator
so:
50/v=(x-50)/y
75/3v=(x-75)/y
I make from that:
(50y/v)+50=x
(25y/v)+75=x
and then i remove fractions and have system of equations
50y+50v=xv
25y+75v=xv *(-2) equivalent adjustment

50y+50v=xv
-50y-150v=-2xv

-100v=-xv
-100=-x
x=100
Now I got the number of steps so if I do 100/2=50 is the number of steps we can see if it is stationary.

I just want to ask if is everything right.
And.. I´m not good in english so there are many mistakes in it, so sorry

I don't see why you divided by 2 at the end.
If only 50 steps are visible, how would B have taken 75 to get to the top?

I don't see how (x-50)/y= 50/v
Same with the one below it.
Y may be any velocity

bamia said:
I don't see how (x-50)/y= 50/v
Same with the one below it.
Y may be any velocity
If A only took 50 steps but rose x steps in the process then the movement of the escalator was responsible for achieving the other x-50 steps in the same time.
A took time 50/v, the escalator took time (x-50)/y.

bamia
Thank you. I get it now.

## What is the significance of the number of escalator steps?

The number of escalator steps is important because it determines the length and height of an escalator, which impacts the overall design and function of the escalator.

## How is the number of escalator steps determined?

The number of escalator steps is typically determined by the rise and run of the escalator, as well as safety regulations and space constraints. Manufacturers use mathematical calculations to determine the optimal number of steps for each escalator.

## What is the average number of escalator steps?

The average number of escalator steps can vary depending on the type and purpose of the escalator. However, most standard escalators have between 24-30 steps, with a rise of around 4-6 inches per step.

## Can the number of escalator steps be changed?

In some cases, the number of escalator steps can be adjusted by adding or removing steps. However, this is a complex and costly process that should only be done by trained professionals to ensure the safety and functionality of the escalator.

## What impact does the number of escalator steps have on energy consumption?

The number of escalator steps can impact the energy consumption of an escalator. A higher number of steps may require more power to operate, while a lower number of steps may result in a more energy-efficient escalator. However, other factors such as speed and weight capacity also play a role in energy consumption.

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