A moving sidewalk runs from Point $A$ to Point $B$. When the sidewalk is turned off (that is, is not moving) it takes Mario 90 seconds to walk from Point $A$ to Point $B$. It takes Mario 45 seconds to be carried from Point $A$ to Point $B$ by the moving sidewalk when he is not walking. If his walking speed and the speed of the moving sidewalk are constant, how long does it take him to walk from Point $A$ to Point $B$ along the moving sidewalk when it is moving?
Suppose that the distance from Point $A$ to Point $B$ is $d \mathrm{~m}$, that Mario's speed is $w \mathrm{~m} / \mathrm{s}$, and that the speed of the moving sidewalk is $v \mathrm{~m} / \mathrm{s}$.

From the given information, $\frac{d}{w}=45$ and $\frac{d}{v}=90$.

The amount of the time, in seconds, that it takes Mario to walk along the sidewalk when it is moving is $\frac{d}{v+w}$, since his resulting speed is the sum of his walking speed and the speed of the sidewalk.

Here,

$$
\frac{d}{v+w}=\frac{1}{\frac{v+w}{d}}=\frac{1}{\frac{v}{d}+\frac{w}{d}}=\frac{1}{\frac{1}{90}+\frac{1}{45}}=\frac{1}{\frac{3}{90}}=30
$$

Therefore, it takes Mario 30 seconds to walk from Point $A$ to Point $B$ with the sidewalk moving.

ANSWER: 30 seconds