Kinematics

\Delta x=15m is the length. t_{w}=90s is the time it takes to
walk on the stalled escalator.t_{s}=60s  is the time it takes to
ride the moving escalator.t_{m} is the time to walk up the moving
escalator.

The walking speed of the person relative to the stalled escalator
is v_{we}=\Delta x/t_{w}.The speed of the escalator relative to
the ground is v_{eg}=\Delta x/t_{s}. The speed of the walking person
relative to the ground on a moving escalator is v_{wg}=\Delta x/t_{m}.
But these three speeds are related: v_{wg}=v_{we}+v_{eg}.

Combine all this:
v_{wg}  =  v_{we}+v_{eg}\\ \frac{\Delta x}{t_{m}}  =  \frac{\Delta x}{t_{w}}+\frac{\Delta x}{t_{s}}\\ \frac{1}{t_{m}}  =  \frac{1}{t_{w}}+\frac{1}{t_{s}}
Put in the numbers and get t_{m}=36s.