Anton ran down a moving escalator and counted 30 steps. Then he decided to run up the same escalator at the same speed relative to the escalator and counted 150 steps. How many steps did he count when descending with a police officer on the stationary escalator?

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Anton ran up 5 times longer than he ran down (because he counted 5 times more steps). At the same time, 5 times more steps came towards him than "ran away" when descending. If Anton runs down 5 times, he will count 150 steps, and the same number of steps will "run away" from him as came towards him during the ascent. Therefore, $150+150$ $=300-$ this is six times the number of steps on the escalator.

## Answer

50 steps.