A metro escalator lifts a passenger standing on it in 1 minute. a passenger climbs a fixed

A metro escalator lifts a passenger standing on it in 1 minute. a passenger climbs a fixed escalator in 3 minutes. How long will it take for a passenger to climb up a moving escalator?

Given:

t1 = 1 minute – the time interval during which the escalator lifts the stationary passenger;

t2 = 3 minutes – the period of time during which the passenger climbs the stationary escalator.

It is required to determine t3 (minute) – the time during which the escalator lifts the passenger walking along it.

Let L be the length of the escalator.

Then the escalator speed will be:

v1 = L / t1.

The passenger’s speed will be equal to:

v2 = L / t2.

When a passenger moves along a moving escalator, their speeds will add up. Then their total speed will be equal to:

v3 = v1 + v2 = L / t1 + L / t2 = L * (t1 + t2) / (t1 * t2).

Let’s find the time:

t3 = L / v3 = L / (L * (t1 + t2) / (t1 * t2)) = t1 * t2 / (t1 + t2) =

= 1 * 3 / (1 + 3) = 3/4 = 0.75 minutes (45 seconds).

Answer: the ascent time will be 45 seconds.