Quiz

Equations relating the length of the escalator to the speeds and the time it takes to traverse it.
X = (v + v_e) * t1 (downwards)
X = (v/2 - v_e) * t2 (upwards)
And for the number of steps:
40 = v * t1
280 = (v/2) * t2
The number of steps, unlike the total distance traveled on the escalator, depends only on the speed relative to the escalator. From the last equations:
t1 = 40/v
t2 = 560/v
Then X = (v + v_e) * 40/v = (v/2 - v_e) * 560/v
40v + 40v_e = 280v - 560v_e
240v = 600v_e
v = 2.5 * v_e
Okay, then:
X = 3.5 * v_e * 40 / (2.5 * v_e) = 3.5 * 16 = 56

56 steps