SOLUTION: A child is running on a moving sidewalk in an airport. When he runs against the sidewalk's motion, he travels 108ft in 27 seconds. When he runs with the sidewalk's motion, he tra

The speed of the child when running with the sidewalk is

     = 12 ft per second = u + v    (1)

where u is the sidewalk's rate and v is the child's rate on a still sidewalk.



The speed of the child when running against the sidewalk is

     =  4 ft per second = u - v    (2)

where u is the child's rate on a still sidewalk and v is the sidewalk rate.



Now you have two equations (1) and (2) for 2 unknowns, u and v.
  
To solve the system, add the equations (1) and (2). You will get

    2u = 12 + 4 = 16  ====>  u = 16/2 = 8 ft/s  is the sidewalk' speed.


Next substitute this found value of u into either equation (1) or (2).

You will find then  ( from (1) )  v = 12 - 8 = 4 ft/s as the rate of the child.


Answer.  Sidewalk's rate is  8 ft/s;  child's rate is 4 ft/s.