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please answer this fast please...!!

it takes 1 minute for a person standing on a moving escalator to reach the top from the ground. If the escalator is not moving , it takes him 3 minutes to walk on the steps to reach the top . how long will it take for the person to reach the top if he walks up the escalator while it is moving..?

Let the speed of the escalator be v steps/minute and the speed of the man be u steps/minute.

Let there be a total of x steps in the escalator

Therefore, as per the information given in the question:

1 = x/v  and 3 = x/u

Therefore, v = x and u = x/3

When the man walks up the escalator, the net speed is v + u = x + x/3 = 4x/3

Therefore, time taken will be x/4x/3 = 3/4 minutes = 45 seconds.

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Let the velocity of the escalator be Ve and the velocity of man on still escalator be Vm.

Let the length of escalator be S

Ve = S/1 = S

Vm = S/3

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When both man and escalator are in motion, their velocities will add up = Vm + Ve = S + S/3 = 4S/3

Time taken = S/ (Vm + Ve)

= S / 4S/3

= 3/4 minutes

or 45 seconds.

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