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 is 2 ​ft/s against the walkway and 8 ft/s with the walkway. What is the​ traveler's speed off the​ walkway? What is the speed of the moving​ walkway? The​ traveler's speed off the walkway is ____ ​ft/s.

Answer 1

The traveler's speed off the walkway is 5 ft/s and the speed of the moving walkway is 3 ft/s, found by setting up a system of equations and solving them simultaneously.

Step-by-step explanation:

To solve for the traveler's speed off the walkway and the speed of the moving walkway, we need to set up a system of equations. Let's denote the traveler's speed off the walkway as x ft/s, and the speed of the walkway as y ft/s.

When the traveler is walking against the walkway, their ground speed is the difference between their walking speed and the walkway's speed. This can be represented as:

x - y = 2 (Equation 1)

When the traveler is walking with the walkway, their ground speed is the sum of their walking speed and the walkway's speed, which can be represented as:

x + y = 8 (Equation 2)

Now we can solve these two equations simultaneously:

• Add Equation 1 and Equation 2: (x - y) + (x + y) = 2 + 8, which simplifies to 2x = 10. Solving for x, we get x = 5 ft/s.
• Substitute x back into Equation 2: 5 + y = 8, solving for y, we get y = 3 ft/s.

Therefore, the traveler's speed off the walkway is 5 ft/s, and the speed of the moving walkway is 3 ft/s.