Henry,’ said the professor’s wife, ‘you’re a mathematician. Tell me how many steps there are in that escalator.’
‘Well, Martha, they certainly are difficult to count while they are moving. But if you will walk up, and count the number of steps you take from bottom to top, I think we can find the answer. I will start with you, but will walk twice as fast. Just watch me and take one step every time I take two.’
When Martha reached the top she reported that she had taken just 21 steps, while Henry had taken 28. The professor was then able to tell her exactly how many steps were in sight at one time on the moving staircase.
How many were there?