Question

A person climbs from a Paris metro station to the street level by walking up a stalled escalator in 96.0 s. It takes 72.0 s to ride the same distance when standing on the escalator when it is operating normally. How long would it take for him to climb from the station to the street by walking up the moving escalator?

Answer 1

41.142 seconds

Step-by-step explanation:

Distance = d

Speed = Distance / Time

Velocity of man

`v_m=(d)/(96)`

`v_e` = Velocity of escalator

`v_e=(d)/(72)`

Velocity of man relative to ground

`v_(mg)=v_m+v_e\\\Rightarrow v_(mg)=(d)/(96)+(d)/(72)\\\Rightarrow v_(mg)=(3d+4d)/(288)\\\Rightarrow v_(mg)=(7d)/(288)\\\Rightarrow (v_(mg))/(d)=(7)/(288)`

Time = Distance / Speed

`\\\Rightarrow (d)/(v_(mg))=(288)/(7)=41.142\ s`

The time it takes for him to climb from the station to the street by walking up the moving escalator is 41.142 seconds