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 1 ft/s against the walkway and 7 ft/s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Let's call the speed of the traveler off the walkway "x" and the speed of the moving walkway "w".
When the traveler walks against the walkway, their speed relative to the ground is:
1 ft/s + w
When the traveler walks with the walkway, their speed relative to the ground is:
7 ft/s + w
Since the traveler's speed off the walkway is the same in both cases (just with opposite directions), we can create an equation:
1 ft/s + w = - (7 ft/s + w)
Solving for w:
1 ft/s + w = -7 ft/s - w
2w = -8 ft/s
w = -4 ft/s
This negative sign just means that the walkway is moving in the opposite direction from the traveler's motion when walking against it.
Now we can find the speed of the traveler off the walkway:
1 ft/s + (-4 ft/s) = -3 ft/s
So the traveler is walking off the moving walkway at a speed of 3 ft/s.
To find the traveler's speed off the walkway, we need to subtract the speed of the walkway from the traveler's speed with the walkway.
Let's assume the speed of the walkway is represented by 'w' ft/s.
The traveler's speed with the walkway is 7 ft/s, and the traveler's speed against the walkway is 1 ft/s. So, we can set up the following equation:
Traveler's speed with walkway - Speed of walkway = Traveler's speed against walkway
7 ft/s - w ft/s = 1 ft/s
To find the speed of the walkway (w), we need to subtract 1 ft/s from both sides:
7 ft/s - 1 ft/s = w ft/s
Therefore, the speed of the walkway is 6 ft/s.
To find the traveler's speed off the walkway, we subtract the speed of the walkway from the traveler's speed against the walkway:
Traveler's speed against walkway - Speed of walkway = Traveler's speed off walkway
1 ft/s - 6 ft/s = -5 ft/s
Hence, the traveler's speed off the walkway is 5 ft/s.