A person climbs an escalator stationary relative to the Earth in 4 minutes. How long will this person climb

A person climbs an escalator stationary relative to the Earth in 4 minutes. How long will this person climb, walking up the moving escalator, if the escalator moves in such a way that it lifts a person standing on it in 2 minutes?

Given:

t1 = 4 minutes – the time during which a person climbs a stationary escalator;

t2 = 2 minutes – the time during which a moving escalator lifts a motionless person.

It is required to determine t (minutes) – how long it will take a moving person to climb along a moving escalator.

Let l be the length of the escalator.

Then the speed of a person will be equal to:

v1 = l / t1.

The escalator speed is:

v2 = l / t2.

The overall speed will be equal to:

v = v1 + v2 = l / t1 + l / t2 = l * (t1 + t2) / (t1 * t2).

That is, the ascent time will be equal to:

t = l / v = l / (l * (t1 + t2) / (t1 * t2)) = l1 * l2 / (l1 + l2);

t = 4 * 2 / (4 + 2) = 8/6 = 1.3 minutes.

Answer: a person will climb a moving escalator for 1.3 minutes.