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?

t = 31.6 s

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