Question

За какое время поднимется идущий вверх пассажир по движущемуся эскалатору,если эскалатор поднимает стоящего на нем пассажира за 3,5 мин. По неподвижному поднимается за 6 мин.

Answer 1

S=vt       t1=6мин=360с
V1=S/t1
V2=S/t2    t2=3,5мин=210с
V1=скорость пассажира
V2=скорость эскалатора    v=v1+v2
(V1+V2)t=S
t=S/v1+v2
t=s/(s/t1+s/t2)=(t1×t2)/(t1+t2)=132,6c=2,2мин

Answer 2

Calculating Time for a Passenger on an Escalator

To calculate the time it takes for a passenger to rise while moving up an escalator, we can use the given information about the time it takes for a standing passenger to rise and the time it takes for a stationary escalator to raise a passenger.

Given Information: - Time for a standing passenger to rise on a moving escalator: 3.5 minutes - Time for a standing passenger to rise on a stationary escalator: 6 minutes

Calculation

To find the time it takes for a passenger to rise while moving up the escalator, we can use the concept of relative speed. When the escalator is moving, the effective speed of the passenger's rise is the difference between the speed of the escalator and the speed of the passenger when standing still.

Let's denote: - Time for a standing passenger to rise on a moving escalator as t1 - Time for a standing passenger to rise on a stationary escalator as t2

The relative speed of the passenger's rise on the moving escalator is given by: Relative speed = Speed of the escalator - Speed of the passenger

Using the formula: Relative speed = Distance / Time

We can calculate the time it takes for the passenger to rise on the moving escalator.

Solution

Given: - Time for a standing passenger to rise on a moving escalator (t1) = 3.5 minutes - Time for a standing passenger to rise on a stationary escalator (t2) = 6 minutes

Using the relative speed concept, we can calculate the time it takes for the passenger to rise on the moving escalator.

Let's denote: - Speed of the escalator as s - Speed of the passenger as p

The relative speed of the passenger's rise on the moving escalator is: Relative speed = s - p

We can use the formula: Relative speed = Distance / Time

Given that the distance is the same for both cases (moving and stationary escalator), we can set up the equation: s - p = Distance / t1 p = s - (Distance / t1)

We can then use the time for a standing passenger to rise on a stationary escalator (t2) to find the speed of the escalator: s - 0 = Distance / t2 s = Distance / t2

Substituting the value of s into the equation for the relative speed: p = (Distance / t2) - (Distance / t1)

We can then solve for the time it takes for the passenger to rise on the moving escalator using the calculated speed of the passenger.

Conclusion

The time it takes for the passenger to rise while moving up the escalator can be calculated using the relative speed concept and the given times for a standing passenger to rise on a moving and stationary escalator.