A person walks up a stalled 15 m long escalator in 110 s. When standing on the same escalator, now moving, the person is carried up in 70 s. How much time would it take that person to walk up the moving escalator?
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To find the time it would take for the person to walk up the moving escalator, we need to analyze the two scenarios given:
1. Person walks up the stationary escalator in 110 s
2. Person is carried up the moving escalator in 70 s
Let's assume that the speed of the person walking is Vw and the speed of the moving escalator is Ve (which is unknown).
In the first scenario, the person walks up the stationary escalator, so the effective speed is just the person's walking speed Vw.
In the second scenario, the person is carried up by the moving escalator, so the effective speed is the sum of the person's walking speed and the speed of the escalator. Therefore, the effective speed is Vw + Ve.
Since the distance covered is the same in both scenarios (15 m), we can set up two equations using the formula: Speed = Distance / Time.
For the first scenario:
Vw = 15 m / 110 s
For the second scenario:
Vw + Ve = 15 m / 70 s
Now, we can solve these two equations simultaneously to find the values of Vw and Ve.
From the first equation:
Vw = 0.136 m/s (rounded to 3 decimal places)
Substituting this value into the second equation:
0.136 m/s + Ve = 15 m / 70 s
Simplifying the equation:
Ve = 15 m / 70 s - 0.136 m/s
Ve = 0.214 m/s (rounded to 3 decimal places)
We have now found the speed of the moving escalator, which is Ve = 0.214 m/s.
Now, to find the time it would take for the person to walk up the moving escalator, we can set up another equation using the formula: Time = Distance / Speed.
Let's assume the time taken to walk up the moving escalator is T.
We know the distance is 15 m and the effective speed being Vw + Ve.
T = 15 m / (Vw + Ve)
T = 15 m / (0.136 m/s + 0.214 m/s)
T = 15 m / 0.35 m/s
T = 42.857 s
Therefore, it would take approximately 42.857 seconds (rounded to 3 decimal places) for the person to walk up the moving escalator.