An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes $$150 s$$ to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in $$70 s$$. Moe boards the sidewalk and walks along it. How long does Moe take to move through the corridor? Assume that Larry and Moe walk at the same speed.
As we konw,The velocity of Larry is $${ v }_{ 1 }$$ and that of Curly is $${ v }_{ 2 }$$. Also, we denote the length of the corridor by $$L$$.
Now, Larry’s time of passage is $${ t }_{ 1 } = 150 s$$ (which must equal $$L/{ v }_{ 1 }$$), and Curly’s time of passage is $${ t }_{ 2 }= 70 s$$ (which must equal $$L/{ v }_{ 2 }$$).
The time Moe takes is therefore $$t=\dfrac { L }{ { v }_{ 1 }+{ v }_{ 2 } } =\dfrac { 1 }{ { v }_{ 1 }/L+{ v }_{ 2 }+L } =\dfrac { 1 }{ \dfrac { 1 }{ 150s } +\dfrac { 1 }{ 70s } } =48s.$$