Solving distance, rate, and time using a set of linear equations

Question

A child is running on a moving sidewalk in an airport. When she runs against the sidewalk's motion, she travels
78ft
in
13
seconds. When she runs with the sidewalk's motion, she travels
156ft
in the same amount of time. What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk?

Answer 1

v1 = velocity of the child

v2 = velocity of the moving sidewalk

 

v1 - v2 = 78 ft/13 secs = 6 ft/sec

v1 + v2 = 156/13 = 12 ft/sec

 

Solve the two equations to get the speed of the child and the moving sidewalk