Question

Эскалатор метро поднимает стоящего на нем пассажира за время t1=6мин, а сам пассажир поднимается по неподвижному эскалатору за время t2=12мин. За какое время поднял бы эскалатор идущего по нему пассажира? Человек двигался в двух последних случаях одинаково.Ответ 4

Answer 1

Дано: t1 = 1 мин; t2 = 3 мин. Найти: t. Решение. Ответ: t = 0, 75 мин

Answer 2

Problem Analysis

We are given that an escalator in a metro station takes 6 minutes to lift a passenger who is standing on it, and the passenger can climb the stationary escalator in 12 minutes. We need to find the time it would take for the escalator to lift a passenger who is walking on it.

Solution

Let's assume that the speed at which the escalator moves is x and the speed at which the passenger walks is y. We can use the formula Speed = Distance / Time to solve this problem.

When the passenger is standing on the escalator, the speed at which the passenger is moving is the sum of the escalator speed and the passenger's walking speed. So we have:

x + y = Distance / t1 (Equation 1)

When the passenger is walking on the stationary escalator, the speed at which the passenger is moving is just the passenger's walking speed. So we have:

y = Distance / t2 (Equation 2)

We can solve these two equations to find the value of Distance and then substitute it into Equation 1 to find the time it would take for the escalator to lift a walking passenger.

Let's solve the equations:

From Equation 2, we have:

Distance = y * t2 (Equation 3)

Substituting Equation 3 into Equation 1, we have:

x + y = (y * t2) / t1

Simplifying the equation, we get:

x = (y * t2) / t1 - y

Now we can substitute the value of x into Equation 2 to find the time it would take for the escalator to lift a walking passenger:

Time = Distance / x

Substituting the value of Distance from Equation 3 and the value of x from the previous equation, we get:

Time = (y * t2) / ((y * t2) / t1 - y)

Simplifying the equation, we get:

Time = (y * t1 * t2) / (y * t2 - y * t1)

Now we can substitute the given values of t1 and t2 into the equation to find the time it would take for the escalator to lift a walking passenger.

Calculation

Substituting t1 = 6 and t2 = 12 into the equation, we get:

Time = (y * 6 * 12) / (y * 12 - y * 6)

Simplifying the equation, we get:

Time = (y * 72) / (y * 6)

The y cancels out, and we are left with:

Time = 72 / 6

Simplifying further, we get:

Time = 12

Therefore, the escalator would take 12 minutes to lift a passenger who is walking on it.

Answer

The escalator would take 12 minutes to lift a passenger who is walking on it.