Man on Stationary Escalator

What was asked to calculate? 

Let L = length of stair , M = Man's speed & E = Elevator's speed.

Let's remind what we have learned in our school days.

Speed = Distance/Time

i.e.

Distance = Speed  x  Time

While moving 'up' along with upward moving elevator, 

30(M+E) = L     ......(1)

While moving 'down' against 'upward' moving elevator, man's speed has to be faster than elevator's speed so that he can reach down at the stair. Otherwise he would never reach down always falling short.

90(M-E) = L    .......(2)

From (1) & (2), we get,

30M+30E=90M-90E

60M=120E

M=2E     .....(3)

E=M/2    .....(4)

Putting (3) in (1),

45M=L

M=L/45    

(Speed=Distance/Time)

Hence man alone needs 45 seconds to climb up that stationary elevator.

Stationary Escalator

Putting (4) in (1), gives,

E=L/90

(Speed=Distance/Time)

So elevator needs 90 seconds to push standing man up.