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.