A metro escalator lifts a passenger who stands on it in 1 minute. Moving along the moving escalator

A metro escalator lifts a passenger who stands on it in 1 minute. Moving along the moving escalator in the direction of its movement, the passenger moves in 45 seconds. How many seconds it takes to move along a standing escalator.

Given:

t1 = 1 minute = 60 seconds – the time interval during which the escalator lifts the passenger standing on it;

t2 = 45 seconds – the time during which the passenger climbs the escalator, moving in the direction of his movement.

It is required to determine t3 (seconds) – the time it takes a passenger to climb a standing escalator.

Let l be the length of the escalator, v1 – the speed of the escalator relative to the ground, v2 – the speed of the passenger relative to the ground. Then:

t1 = l / v1, hence: v1 = l / t1

t2 = l / (v1 + v2), hence v1 = l / t2 – v2. Then:

l / t1 = l / t2 – v2;

v2 = l / t2 – l / t1 = l * (t1 – t2) / (t1 * t2).

t3 = l / v2 = l / (l * (t1 – t2) / (t1 * t2)) = t1 * t2 / (t1 – t2) = 60 * 45 / (60 – 45) =

= 2700/15 = 180 seconds.

Answer: a passenger will climb a standing escalator in 180 seconds.