Problem

Sonia walks up an escalator which is going up. When she walks at one step per second, it takes her 20 steps to get to the top. If she walks at two steps per second, it takes her 32 steps to get to the top. She never skips over any steps. How many steps does the escalator have?

Solution (Mehmet Şamil Çelik from Turkiye)

Let $V$ be the velocity of escalator in steps per second. Then, the total number of steps of escalator can be given for two different situations as follows:

$$ 20 (V + 1) = 16 (V + 2)

$$

Therefore we have $V = 3$ (measured in steps/sec). This also gives us the total number of escalator steps as $80$ if we substitute in the above formulae.

Thank you!

Special thanks to Mehmet Şamil Çelik (Turkiye), Or Eliyahu (Israel), Jack (Richmond), Ravi Dayabai (California) and Conrad Warren (Alberta, Canada) for submitting a solution to this challenge problem.