Question

A person takes T1 second on the stationary escalator to cover some distance. The person takes T2 second in the moving escalator to cover same distance by same velocity. If the person is at rest on the escalator then time taken by him to cover same distance is?

Answer 1

Let the length of escalator is L.
Then, velocity of man = distance/time taken = L/T₁
Velocity of man with respect to escalator = L/T₂
so, velocity of escalator with respect to man = -L/T₂
We know,
velocity of escalator = velocity of escalator with respect to man + velocity of man
L/T = -L/T₂ + L/T₁ = L/(1/T₁ - 1/T₂)
T = T₁T₂/(T₂ - T₁)

Answer 2

Let L be the distance or length from the ground to top of escalator.

Velocity of man by walk = Vman=speed /distance =L/T1

Velocity of man with respect to escalator: VMe=L/T2

Veloicity of escalotor w.r.t man= -Vme =-L/T2

Velcoty of escalator= Velocity of Man + Velocity of escalotor w.r.t man.
L/T= L/T1-L/T2
1/T=1/T1-1/T2

1/T=T2-T1/T1T2
T=T1T2/T2-T1

∴Time taken to reach same distance
=T1T2/(T2-T1 )