Answer:
41.142 seconds
Explanation:
Distance = d
Speed = Distance / Time
Velocity of man
[tex]v_m=\frac{d}{96}[/tex]
[tex]v_e[/tex] = Velocity of escalator
[tex]v_e=\frac{d}{72}[/tex]
Velocity of man relative to ground
[tex]v_{mg}=v_m+v_e\\\Rightarrow v_{mg}=\frac{d}{96}+\frac{d}{72}\\\Rightarrow v_{mg}=\frac{3d+4d}{288}\\\Rightarrow v_{mg}=\frac{7d}{288}\\\Rightarrow \frac{v_{mg}}{d}=\frac{7}{288}[/tex]
Time = Distance / Speed
[tex]\\\Rightarrow \frac{d}{v_{mg}}=\frac{288}{7}=41.142\ s[/tex]
The time it takes for him to climb from the station to the street by walking up the moving escalator is 41.142 seconds
