Systems Of Equations Word Problem

Question

A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed against the walkway is 3ft/s and 7ft/s with the walkway? What is the traveler's speed off the walkway? What is the speed of the moving walkway?

Answer 1

Let X be the speed of the traveler, let W be the speed of the walkway:

X - W = 3
X + W = 7

(subtract the speed of the walkway when the traveler is moving against it, add it when the traveler is moving with it)

add the two equations together:

(X - W) + (X + W) = 3 + 7
2X = 10
X = 5

Use either original equation to get W = 2

So the traveler is moving at 5 ft / sec and the walkway at 2 ft / sec.