Chapter A.8, Problem 30AYU

To determine

To find: Toronto’s Pearson international Airport has a high-speed version of a moving walkway. If Liam walks while riding this moving walkway, he can travel 280 meters in 60 seconds less time than if he stands still on the moving walkway. If Liam walks at a normal rate of $\text{1}\text{.5}$ meters per second. what is the speed of the walkway?

Answer to Problem 30AYU

The speed of walkway is 2 m/sec.

Explanation of Solution

Given:

Toronto’s Pearson international Airport has a high-speed version of a moving walkway. If Liam walks while riding this moving walkway, he can travel 280 meters in 60 seconds less time than if he stands still on the moving walkway. If Liam walks at a normal rate of $\text{1}\text{.5}$ meters per second.

Calculation:

He walks $\text{1}\text{.5 m}/\text{sec}$.

The walkway has $x\text{ m}/\text{sec}$.

$\frac{280}{1.5+x}$ is the time it takes him to do it while walking. The units are seconds.

That is 60 seconds fewer than $\frac{280}{x}$, the time it takes him without walking.

Therefore $\frac{280}{1.5+x}+60=\frac{280}{x}$, meaning that the time by walking is 60 seconds less than by standing.

$\frac{280+90+60x}{1.5+x}=\frac{280}{x}$

$420+280x=370x+60x^2$

$60x^2+90x-420=0$

$2x^2+3x-14=0$

$\left(2x+7\right)\left(x-2\right)=0$

$x=2 \text{m}/\text{sec}$, only positive root.