As you hurry to catch your flight at the local airport, you encounter a moving walkway that is 85 m long and has a speed of 2.2 m/s relative to the ground. If it takes you 68 s to cover 85 m when walking on the ground, how long will it take you to cover the same distance on the walkway? Assume that you walk with the same speed on the walkway as you do on the ground.

I got that answer to be 24.6 seconds.

Then the next part asks how long would it take you to cover the 85-m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.3 m/s relative to the walkway?
Do I just subtract 1.25(The speed of someone walking next to the belt) from 1.3 and then do (85m/.05mps)?

To solve this problem, you need to consider the relative speeds of the walkway and your walking speed.

Let's first calculate the time it takes you to cover the distance on the walkway when you walk with the same speed as on the ground.

Given:
Length of the walkway (L) = 85 m
Speed of the walkway (Vw) = 2.2 m/s
Time taken on the ground (Tg) = 68 s

The speed of walking on the ground is the relative speed of your walking speed and the walkway's speed, which is (2.2 m/s - 0 m/s) = 2.2 m/s.

To cover the distance on the walkway (L) at a speed of 2.2 m/s, we can use the formula:
Time (T) = Distance (D) ÷ Speed (S)
T = L / S
T = 85 m / 2.2 m/s
T ≈ 38.64 s

Therefore, it would take you approximately 38.64 seconds to cover the 85-meter length of the walkway, assuming you walk with the same speed as on the ground.

Now, let's consider the situation where you turn around and start walking in the opposite direction on the walkway, with a speed of 1.3 m/s relative to the walkway.

To find the time taken in this scenario, we need to consider the relative speed of your walking speed and the walkway's speed. The relative speed is the difference between your walking speed and the walkway's speed.

Relative speed (Rs) = Walking speed - Walkway's speed
Rs = 1.3 m/s - 2.2 m/s
Rs = -0.9 m/s

Since the relative speed is negative (-0.9 m/s), it means you are walking in the opposite direction to the walkway's motion.

To calculate the time taken, we can again use the formula:
Time (T) = Distance (D) ÷ Speed (S)
T = L / S
T = 85 m / (-0.9 m/s)
T ≈ -94.44 s

The negative sign indicates that the time taken is negative, which is not physically meaningful in this context. It suggests that you would need to walk at a faster speed relative to the walkway to cover the distance in the opposite direction.

Therefore, in this scenario, you would not be able to cover the 85-meter length of the walkway while walking in the opposite direction with a speed of 1.3 m/s relative to the walkway.

To solve the second part of the question, let's break it down step by step:

1. First, calculate the effective velocity of the person relative to the ground when walking in the opposite direction to the walkway. This can be found by subtracting the velocity of the walkway, which is 2.2 m/s, from the velocity of the person relative to the walkway, which is 1.3 m/s. Therefore, the effective velocity relative to the ground is 1.3 m/s - 2.2 m/s = -0.9 m/s. Note that the negative sign indicates that the person is walking in the opposite direction to the walkway.

2. Now, we need to calculate how long it will take the person to cover the 85 m length of the walkway with this effective velocity. We can use the formula: time = distance / velocity. Substituting the values, we have time = 85 m / (-0.9 m/s). Remember to use the negative value since the person is walking in the opposite direction.

3. Calculating this, we find that time = -94.44 s. However, time cannot be negative in this context, so we take the absolute value to make it positive. Therefore, the answer is approximately 94.44 seconds.

Note: The answer may seem counterintuitive since the person is walking in the opposite direction, but the negative effective velocity results in a positive time value. This indicates that it will take approximately 94.44 seconds for the person to cover the 85 m length of the walkway when walking in the opposite direction relative to the walkway.