it takes 1 min to a passenger standing on a escalator to reach the top.if the escalator does nt move it takes him 3 mins to walk up.how long will it take or the passenger to arrive at the top if he walks up the moving escalator?.....................i am getting 90 sec....whereas the real ans is 45 sec......

Let the distance to the top be D. So the speed of the man with escalator moving = (D/1) m/min. Therefore the speed of the man with the escalator at rest = (D/3) m/min. When both the man and the escalator are moving, effective speed= (D/3 + D) m/min =(4D/3)m/min .Therefore time taken when both man and escalator are moving,Time = distance / speed          = D/(4D/3) min.           = 3/4 min           = 45 seconds