Walking Up the Escalator

Date: 6/14/96 at 14 22:23:56 
From: Anonymous
Subject: Word problem!

Hi Dr. Math,

I really thank you for taking the time to read this. Here is my 
problem: 

An escalator and a staircase have the same step length, width, and 
height, and the same number of steps (i.e, the same length). It takes 
ten seconds to walk up the stairs (assuming that you don't trip or 
skip step or pause) and eleven seconds to go up the escalator 
(assuming that you do none of the things you wouldn't do on the 
stairs, or push emergency buttons and such). 

How long does it take to get to the top if you walk up the escalator 
while it is moving in the right direction? (ASSUMING you would 
do none of the above and there is no one else in the way.) 

This would help me out a lot, and it's been bugging me for a long 
time. 

Thank you for your help,

Samira Azzam (7th grade)

Date: 6/15/96 at 11:14:01 
From: Dr. Anthony
Subject: Re: Word problem!

With these problems you have to let distances and speeds be 
represented by letters so that you can write down equations to 
describe what is happening. 

Let s = distance up the stairway
u = speed of escalator
v = speed you walk up the stairway

Now we have time = distance/speed, and so 

s/u = 11 s/v = 10

u = s/11	v = s/10

When walking on the moving escalator the total speed = u+v 

so total speed = s/11 + s/10 = (21/110)s 

Time when walking on the moving escalator = s/(u+v) 

= s/((21/110)s)

= 110/21

= 5 + 5/21 seconds

-Doctor Anthony, The Math Forum