A person climbs from a Paris metro station to the street level by walking up a stalled escalator in 96.5 s. It takes 60.0 s to ride the same distance when standing on the escalator when it is operating normally. How long would it take for him to climb from the station to the street by walking up the moving escalator?
To find the time it would take for the person to climb from the station to the street by walking up the moving escalator, we need to first calculate the person's walking speed and the speed of the escalator.
Let's assume the distance from the station to the street is "d".
When the escalator is stationary, the time it takes to climb up is given as 96.5 s. In this case, the person is essentially walking up the escalator while the escalator is not moving.
We can compute the person's walking speed "v" using the formula:
v = d / t,
where "t" is the time to climb.
Using the given values, we have:
v = d / 96.5.
Now, when the escalator is moving, it takes 60.0 s to cover the same distance from the station to the street.
The combined speed of the person walking and the moving escalator is equal to the distance divided by the time taken:
v_total = d / 60.0.
We need to find the new time it would take for the person to climb from the station to the street by walking up the moving escalator. Let's call this time "t_new".
Using the combined speed formula, we have:
v_total = d / t_new.
Since the person's walking speed when the escalator is stationary is the same as when it is moving, we can equate the two formulas:
d / 96.5 = d / t_new.
Now, we can solve this equation for "t_new":
t_new = (96.5 * 60.0) / 60.0.
By plugging the values into the equation, we get:
t_new = 96.5.
Therefore, it would still take 96.5 s for the person to climb from the station to the street by walking up the moving escalator.
To find out how long it would take for the person to climb from the station to the street by walking up the moving escalator, we need to determine the speed at which the escalator is moving.
Let's denote the speed of the person walking as Vw, and the speed of the escalator as Ve.
When the person walks up the stalled escalator, their speed relative to the escalator is equal to their walking speed. When the person walks up the moving escalator, their speed relative to the escalator is the difference between their walking speed and the speed of the escalator.
We can use the formula: Speed = Distance / Time
For the person walking up the stalled escalator:
Vw = Distance / Time1
where Time1 = 96.5 seconds
For the person riding the escalator:
Vw + Ve = Distance / Time2
where Time2 = 60 seconds
We need to find the Time3 it would take for the person to climb from the station to the street by walking up the moving escalator. The distance covered in all three scenarios is the same.
When the person walks up the moving escalator:
Vw - Ve = Distance / Time3
We can rewrite the formula for the person walking up the moving escalator as:
Distance = (Vw - Ve) * Time3
We can equate the distances covered in all three scenarios:
(Vw - Ve) * Time3 = Vw * Time1 = (Vw + Ve) * Time2
Now, we can solve for Time3:
(Time3 * (Vw - Ve)) = (Time2 * (Vw + Ve)) / Time1
Time3 = ((Time2 * (Vw + Ve)) / Time1) / (Vw - Ve)
Substituting the given values:
Time3 = ((60 * (Vw + Ve)) / 96.5) / (Vw - Ve)
Since the question does not provide the specific values for the walking speed Vw and the speed of the escalator Ve, we can only express the time it would take for the person to climb from the station to the street by walking up the moving escalator in terms of Vw and Ve.