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?

This one is just math ...

The rate of the escalator, r steps per second, is assumed to be constant. If the escalator were stopped, there would be a certain number of steps or distance to travel. I called that distance d.

That distance is the same all three days and therefore we have 2 equations to set up. The total distance covered is the same each trip all three days.

Day one took me 30 seconds to get to the top and day two took me half of 36 or 18 seconds.

So on day one
d steps = 30 steps + r(30 seconds)

on day two
d steps = 36 steps + r steps/second(18 seconds)

simply subtract one equation from the other to get
0 = -6 steps + 12 steps r
6 = 12 r
1/2 = r

To check it, you go half a step per second on the escalator at its own rate, so on day one in 30 seconds he went 15 steps by the escalator's rate only, plus the 30 he climbed, that's 45 steps.

On Day Two, the escalator takes him 9 steps in 18 seconds, and he climbed 36, so there are 45 steps. BINGO. He's tired, the escalator takes 90 seconds to get him up the 45 stairs at half a stair per second. The end.

Posted by Lawrence on 2003-08-24 19:08:53