Walking down the escalator
A man walks down an escalator that is itself moving down. Taking 26 steps, he reaches the bottom in 30 seconds. Walking faster, he takes 34 steps and reaches the bottom in 18 seconds. The escalator moves at a constant rate, and so does he on each trip.
How many steps are visible on the escalator?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
The visible steps are covered partly by the man's own steps and partly by the escalator's motion.
If the escalator moves steps per second and there are visible steps, then .
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. On each trip, the visible steps are shared between the steps the man takes and the steps the escalator carries him. Two trips give two equations for two unknowns.
Step 1: the equations. With visible steps and the escalator moving steps per second:
Step 2: solve. Subtracting, , so step per second, and
Check. . So 46 steps are visible.