Question

When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 43 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 79 s to travel the same distance.

How long will it take you to travel from the gate to baggage claim if you walk while riding on the moving sidewalk?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Let's say the distance from gate to baggage claim be x.

So, Speed of sidewalk = $\frac{Distance}{Time}=\frac{x}{79}$

My Speed = $\frac{Distance}{Time}=\frac{x}{43}$

Now, when I'm walking on moving sidewalk, total speed = $\frac{x}{79}+\frac{x}{43}$

So, Time taken for same distance =$\frac{Distance}{Time} = \frac{x}{\frac{x}{79}+\frac{x}{43}}$

=$\frac{x}{x\left ( \frac{1}{79}+\frac{1}{43} \right )}$

= $\frac{79 \times 43}{79+43} = 28 s$