Answer
$t = 38.8~s$
Work Step by Step
Let $d$ be the distance the person moves along the escalator.
We can find the person's climbing velocity $v_p$ on the stalled elevator:
$v_p = \frac{d}{94~s}$
We can find the escalator's moving velocity $v_e$:
$v_e = \frac{d}{66~s}$
We can find the person's velocity $v$ when walking along the moving escalator:
$v = v_p+v_e = \frac{d}{94~s}+\frac{d}{66~s}$
We can find the time it would take to walk up the moving escalator:
$t = \frac{d}{v} = \frac{d}{\frac{d}{94~s}+\frac{d}{66~s}}$
$t = \frac{1}{\frac{66~s+94~s}{(94~s)(66~s)}}$
$t = \frac{(94~s)~(66~s)}{66~s+94~s}$
$t = 38.8~s$
