.
Let L be the escalator length, in some units of length.
Let "u" be the Marty's rate walking on unmoving escalator, in consistent units of length per second.
Let "v" be the escalator rate, in the same units.
Then from the condition,
L = 30*v (1) ("If Marty stands on it, it takes 30 seconds to reach the 2nd floor")
and
L = 12*(u + v) (2) ("If he walks while the escalator is moving, it takes him 12 seconds.")
From these equation
v = (3)
u + v = (4)
Subtract equation (3) from equation (4). You will get
u = - = = = .
Thus we learned that the Marty' rate is units of length per second.
The problem asks "how long does it take if he walks up to the 2nd floor on the escalator while the escalator is not moving".
This time is the distance L divided by the Marty' rate , i.e.
time = = 20 seconds. ANSWER
ANSWER. 20 seconds.
Solved.
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Do you understand the solution in full ?
In order for you do understand it even better, I will tell you that this "Travel & Distance" problem
is an exact analogue to "Joint work problem", where Marty is one of two participants and escalator is the other participant.
The distance L is then the job which they make together,
while their rates are "rates of work" in an corresponding "Joint work problem".
I recommend you to read and re-read this solution at least thrice.