Achild is running on a moving sidewalk in an airport. when he runs against the sidewalk's motion, he travels
84ft
in
14
seconds. when he runs with the sidewalk's motion, he travels
70ft
in
7
seconds. what is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk?

Rate=distance/time
Rate of the child when he runs aginst the side walk´s motion
rate=84 ft/14 s=6 ft/s

Rate of the child when he runs with the sidewalk´s motion.
rate=70 ft/7s=10 ft/s

rate of the moving sidewalk=x
rate of the child=y

We can suggest this system or equations_
y+x=10
y-x=6

We can solve this system of equations by reduction method. 

y+x=10
y-x=6

2y=16        ⇒y=16/2=8

  y+x=10
-(y-x=6)

     2x=4            ⇒x=4/2=2

The rate of the child would be 8 ft/s and the rate of the sidewalk´s motion would be 2 ft/s.