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?
Another way to solve it is by time = distance / velocity. Let x be the height and u the speed of the escalator, and v the man's speed at one step per second. On the first day we have:
x/(u+v)=30 seconds
And on the second day:
x/(u+2v)=18 seconds (36 steps at 2 steps per second).
Rearrange the first equation we get:
v = x/30 - u,
and plugging that into the second equation we get:
u = x/90.
If the man sits down, his speed is u, and the time it takes him is:
x/u = x/(x/90) = 90 seconds.
Reassuringly, that's the same answer Charlie got!
another solution
