Final answer:
The problem involves calculating the time it takes for a person to walk up a moving escalator using relative motion equations. We find the speed of the person and the escalator from given conditions and use these to solve for the desired time.
Step-by-step explanation:
The problem at hand is a classic example of relative motion and can be solved using algebra. When the person walks up the stalled escalator, it takes him 90 seconds. When the escalator is moving, it carries him up in 60 seconds without walking. The question is to find out how much time it would take for the person to walk up the moving escalator.
Let's denote the time it would take for the person to walk up the moving escalator as t. The speed of the person walking is the same in both cases. We can define two speeds, speed of the person (vp) and speed of the escalator (ve). The distance covered by the escalator in 60 seconds is the same as the distance the person walks in 90 seconds. Therefore, we can set up two equations representing these conditions:
- Distance = vp * 90
- Distance = (vp + ve) * 60
We can then find a relationship between vp and ve using these equations. Once these speeds are determined, we can find the time it takes for the person to walk up the moving escalator using the equation:
Solving this system of equations will yield the desired value of t, the time to walk up the moving escalator.