Question

An airport terminal has a moving sidewalk to speed passengers through a long corridor. Larry does not use the moving sidewalk; he takes $\mathbf{150}\mathbf{}\mathbf{s}$ to walk through the corridor. Curly, who simply stands on the moving sidewalk, covers the same distance in $\mathbf{70}\mathbf{}\mathbf{s}$. 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.

Short answer

Time to move through the corridor is$48\mathrm{s}$

Step-by-step solution

Given information

$$\begin{gathered} {\mathrm{t}}_1=150\mathrm{s} \\ {\mathrm{t}}_2=70\mathrm{s} \end{gathered}$$

Determining the concept

Use basic definition of velocity to find the answer of the given problem. Velocity is total displacement divided by time.

Formula:

$\mathrm{v}=\frac{\mathrm{d}}{\mathrm{t}}$ (i)

Where, d is total displacements, v is an initial velocity and t is time.

Determining the time to move through the corridor

Now,

Using equation (i), the time can be written as,

${\mathrm{t}}_1=\frac{\mathrm{d}}{{\mathrm{v}}_1}$

and

${\mathrm{t}}_2=\frac{\mathrm{d}}{{\mathrm{v}}_2}$

Total time T is given as,

$\mathrm{T}=\frac{\mathrm{d}}{{\mathrm{V}}_1+{\mathrm{V}}_2}$

Now, plug the values of v₁and v₂,

$\mathrm{T}=\frac{\mathrm{d}}{\frac{\mathrm{d}}{{\mathrm{t}}_1}+\frac{\mathrm{d}}{{\mathrm{t}}_2}}$

So,

$\mathrm{T}=\frac{1}{\frac{1}{{\mathrm{t}}_1}+\frac{1}{{\mathrm{t}}_2}}$

$\mathrm{T}=\frac{1}{\frac{1}{150}+\frac{1}{70}}$

So,$\mathrm{T}=48\mathrm{s}$