Number of Steps on a Stationary Escalator with Varying Person Speeds

[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.?

Homework Equations

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

 

[RUber]

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?

 

[bamia]

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

 

[haruspex]

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.