Mechanics and Logic
Important: This problem can be solved without equations or formulas or variables of any kind. It is more on developing logical thinking and reasoning, an impoortant part of maths.
A passenger can walk up a stationary escalator in 3 minutes. If this very same escalator is moving, however, and the passenger is still walking upwards with the same speed, he will be at the top in 2 minutes. Will he be able to walk up an escalator which is moving at the same speed downwards (i.e. in the opposite direction to the passenger's direction of motion)? If so, then how long would it take him to reach the top?
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We can see that when the passenger was moving upwards, he got to the top faster. Therefore, we conclude that the passenger was moving faster than the escalator. If so, then he will be able to go up an escalator which is moving downwards. That eliminates the "No" option.
How long will it take him? Well, 6 minutes, because the escalator covers a third of its length in 2 minutes, (it covered one-third of the way when the passenger was moving upwards with it). The passenger walks up for 2 minutes, covering two-thirds of the way: the escalator pushese him down one-third of the way. So, in 6 minutes, he will have reached the top.