### 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 $t_{m}=36s$.