A man walks up an escalator, taking one step per second. After taking thirty steps, he is at the top.

Next day, he goes up at two steps per second, reaching the top in 36 steps.

The third day, he has had a long afternoon and merely sits on the escalator, waiting for it to reach the top.

How long does it take him?

At the rate of one step per second, it takes the man 30/1 = 30 seconds to reach the top.

At the rate of two steps per second, he reaches the top in 36/2 = 18 seconds.

Let the rate of the escalator be r steps per second.

Then, by the problem,

30(r+1) = 18(r+2), giving:

r = 0.5, so that:

The total number of steps in the escalator is 30*1.5 = 45

Consequently, if the man does not move, it would take the escalator precisely 45/0.5 = 90 seconds to carry him to the top.

*Edited on ***October 26, 2007, 5:21 am**