Answer: t3 = 45sec.
Explanation:
The equations of motion for the three cases mentioned are
S = v1t1; S = v2t2; S = (v1 + v2)t3,
where S is the length of the escalator, v1 the speed of the escalator, v2 the speed of the passenger on the stationary escalator, t1 the time it takes the passenger standing still on the escalator to travel from the bottom to the top, t2 the time it takes the passenger to walk up the stationary escalator, t3 the time it takes the passenger to walk up the moving escalator.
Solving this set of equations, we find the time we are seeking:
t3 = t1t2/(t1 +t2) = 45sec.