Question

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.

Answer 1

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 $$t=\dfrac { L }{ { v }_{ 1 }+{ v }_{ 2 } } =\dfrac { 1 }{ { v }_{ 1 }/L+{ v }_{ 2 }+L } =\dfrac { 1 }{ \dfrac { 1 }{ 150s } +\dfrac { 1 }{ 70s } } =48s.$$