Problem $4$

A people mover system serves two areas on main campus whose dimensions are illustrated in Figure $4-1.$

As usual, the stops are located at the centers of the service areas.

Assume that all locations in the areas are equally likely to be destinations for passengers traveling from

West Campus $($Stop $0).$ and that the expected walking distance $($E$[$distance$])$ is $300$ m if a passenger

alights at Stop $1$ and $250$ m if a passenger alights at Stop $2.$ Use these values even if I made a mistake.

That is$,$ do not take time to recalculate them.

Figure $4-1$: Illustration of areas served by people mover systems considered in Problem $4($not to scale$)$

a$.(5$ pts $)$ What is the expected walking distance, in meters, for a random passenger boarding at Stop $0?$

Present your answer to the nearest meter.

b$.(5$ pts$)$ Assume that a passenger alights at Stop $1$ and walks with speed Vped $=1\mathrm{.}5[\frac{m}{s}].$ What is the

maximum $($greatest$)$ walking time to the nearest second for this passenger if the passenger walks with

i$.$ Rectilinear distance

ii$.$ Straight line $($Euclidean$)$ distance