Solution:

Let the length of the escalator be \(L\). Speed of person is \(v_p = L/45\). Speed of escalator is \(v_e = L/60\). When both move, their effective speed is \(v_{eff} = v_p + v_e = L/45 + L/60 = (4L+3L)/180 = 7L/180\). The time taken \(T = L/v_{eff} = L / (7L/180) = 180/7 \approx 25.71\) s.