Question 927340
Let the speed of the escalator be {{{u(stairs/second)}}}. 

John took {{{15steps}}} on the way up and took {{{12}}} seconds to reach the top.
 
Mary took only {{{7}}} steps up, and took {{{18}}} seconds.


Since the length of the escalator is constant: 


{{{15stairs +12second*u = 7stairs + 18second*u}}} => 


{{{15stairs - 7stairs=18*u-12second*u}}} 


{{{8stairs=6second*u }}}


{{{8stairs/6second=u }}}


{{{u= (4/3)( stairs/ second)}}}


Therefore, the total length of the escalator:


 {{{15stairs +12*u}}}


 ={{{15stairs +cross(12)4cross(second)*(4/cross(3))( stairs/ cross(second))}}}  


={{{15stairs +4*4stairs}}} 


={{{15stairs +16stairs}}} 

={{{31stairs}}}


answer is: D) {{{31}}}