I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom,
can you tell the height of the stair way in steps?
Let speed of the escalator be x steps per second.
In 30 second the escalator will come down by 30 x steps and in 18 seconds it will come down by 18 x steps.
Since height of the stair way is same 26 + 30(x) = 34 + 18(x)
x = 2/3.
Height of the stair way = 26 + 30 (2/3)
= 46 steps.