An escalator (moving staircase) of n uniform steps visible at all times descends at constant speed. Two boys, A and Z, walk down the escalator steadily as it moves, A negotiating twice as many escalator steps per minute as Z. A reaches the bottom after taking 27 steps while Z reaches the bottom after taking 18 steps. Then n is:
a) 63
b) 54
c) 45
d) 36
e) 30
https://artofproblemsolving.com/wiki/index.php/1965_AHSME_Problems
Problem 28
this question does not have an answer on AoPS. Can someone please help me, I am stuck.