Question

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 86 s to travel the same distance. Part A How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Answer 1

To find the time it would take to walk on the moving sidewalk, calculate the combined speed as the sum of walking speed and moving sidewalk speed. Then divide the distance by the combined speed. It will take approximately 31.6 seconds to travel the distance while walking on the moving sidewalk.

Step-by-step explanation:

Calculating Time When Walking on a Moving Sidewalk

To determine how long it will take to travel from the gate to baggage claim if you walk while riding on the moving sidewalk, we need to utilize the concept of relative speed. When you walk on the stationary sidewalk, it takes you 50 seconds, and when you stand on the moving sidewalk it takes 86 seconds. These two pieces of information allow us to calculate the combined speed when doing both actions simultaneously.

Let's define the speeds as follows:

• Walking speed (W): distance covered in 50 seconds when the sidewalk is broken.
• Moving sidewalk speed (M): distance covered in 86 seconds when standing still on the working sidewalk.

We can assume the distance (D) to baggage claim is the same in both scenarios, thus:

• D = W × 50
• D = M × 86

By combining these speeds, we can find the time it would take when walking on the moving sidewalk:

• Combined speed (C) = Walking speed (W) + Moving sidewalk speed (M)

Since D = W × 50 = M × 86, we find W = D / 50 and M = D / 86. Substituting these into the combined speed equation gives:

• C = (D / 50) + (D / 86)

Finally, to find the time (T) to travel the same distance D at combined speed C, we use:

• T = D / C

Combining all the expressions, we get:

• T = D / ((D / 50) + (D / 86))

After simplifying:

• T = 1 / ((1 / 50) + (1 / 86))

Calculating T, we find:

• T ≈ 1 / ((1 / 50) + (1 / 86))
  
• T ≈ 1 / (0.02 + 0.011627907)
  
• T ≈ 1 / (0.031627907)
  
• T ≈ 31.6 seconds (to two decimal places)

Therefore, it will take approximately 31.6 seconds to travel from the gate to baggage claim if you walk while riding on the moving sidewalk.

Answer 2

t = 31.6 s

Step-by-step explanation:

In the exercise when he walks, as when going on the mobile sidewalk the speed is constant, so we can use the equations of motion

v = d/t

We have two situations

Walking

v1 = d / t1

On the mobile sidewalk

v2 = d / t2

He is raised on the sidewalk walked, this does not change the speed of either

vt = v1 + v2

We substitute and calculate

d / t = d /t1 + d /t2

1 / t = 1 / t1 + 1 / t2

1 / t = 1/50 + 1/86

1 / t = 0.02 + 0.0116

t = 31.6 s

You can see that as expected the time is less with greater speed