Howard walks 2 steps each second, and Bobby walks 3
steps each second.
They are going the wrong way, up the down escalator. Suppose the escalator
moves x steps per second. Then the escalator slows them down by x steps per
second.
Howard walks 2 steps each second, and Bobby walks 3 steps each second.
So Howard's actual rate on the moving escalator is 2 - x steps/second,
And Bobby's actual rate on the moving escalator is 3 - x steps/second
It takes Howard 60 seconds while it takes Bobby 30 seconds to get to the 2nd
floor.
distance = rate∙time, so
Howard's distance (in steps) = Bobby's distance (in steps), so
60(2 - x) = 30(3 - x)
Solve that, get x = 1 steps/second, the speed of the escalator.
distance = rate∙time, so 60(2 - 1) = 60(1) = 60 steps = height of the
escalator in steps = the distance between the two floors, in escalator
steps.
How long does it take them to walk to the 2nd floor if the escalator is not moving?
Howard's time to go 60 steps at the rate 2 steps/second on the stopped
escalator = distance/rate = 60/2 = 30 seconds.
And Bobby's time to go 60 steps at the rate 3 steps/second on the stopped
escalator = distance/rate = 60/3 = 20 seconds.
Edwin