A person walks up a stalled escalator in 25 s. When standing on the same escalator, now moving, she is carried up in 16 s. How much time in seconds would it take her to walk up the moving escalator?

Wow !  This is one that I had to think about overnight, and it's one that I'll carry with me to fascinate other people with.  Here's how I finally decided to approach it:-- Walking up the escalator when it's not operating, she climbs 1/25 = 0.04 of the total height each second.-- When it's operating and she's standing on it, the step that she's standing on climbs 1/16 = 0.0625 of the total height each second.-- When it's operating AND she's walking, she climbs (0.04 + 0.0625) = 0.1025 of the total height each second. 0.1025 height per second = 1 / 0.1025 = 9.756 seconds per height.