#### Answer

It would take 30 seconds if the person walks while the sidewalk is moving.

#### Work Step by Step

Let $v_w$ be the person's walking speed.
Let $v_s$ be the speed of the moving sidewalk.
Let $d$ be the distance traveled along the walkway.
We can set up two equations of the form $v = \frac{d}{t}$
$v_w = \frac{d}{50~s}$
$v_s = \frac{d}{75~s}$
We can set up an equation for the combined speed.
$v_w+v_s = \frac{d}{50~s}+\frac{d}{75~s}$
$v_w+v_s = \frac{3d}{150~s}+\frac{2d}{150~s}$
$v_w+v_s = \frac{5d}{150~s}$
$v_w+v_s = \frac{d}{30~s}$
It would take 30 seconds if the person walks while the sidewalk is moving.