A person runs down a subway escalator in a time t1 = 1 min, and runs up in a time t2 = 5 min.

A person runs down a subway escalator in a time t1 = 1 min, and runs up in a time t2 = 5 min. How long does it take for the person standing on the escalator to descend?

We are given:
t1 = 1min
t2 = 5 min
Decision:
Denoting s the length of the escalator, v – its speed, and х – the speed of a person, from the condition we obtain the system
s / (v + x) = 1
s / (v + 2x) = 3/4
whence v = 2/3 s,
t = s / v = 3/2, i.e. the person standing on the escalator descends for 1.5 minutes
Answer: t = 1.5 min