Moving Walkways

I think this problem is just similar to boat and river, that boat going upstream and boat going downstream problems. When Karen walks with the movement of the walkway, it is similar to boat going downstream and with Karen in the direction against the walkway, it is similar to boat going upstream.
 

Fundamentally, this problem is about motion with constant speed with formula $s = vt$. For speed $v$, use the net speed. For more details details, check the motion in a current of water or air.
 

Let $x$ = Karen’s normal walking speed
$t_\text{50' with the walkway} + t_\text{50' against the walkway} = 40 \text{ sec}$

$\dfrac{50}{x + 2.5} + \dfrac{50}{x - 2.5} = 40$

$x = 4.045 \text{ ft/sec}$
 

Important:
Tell Karen not to walk against the walkway. For her safety and for the safety of other people using the walkway, she must alight first then look for another walkway in opposite direction for her to go back. :)