Dr. Abner Mallity (Advisor to Willy Nilly and Millie Farad) has been doing some consulting River City Circuits Corporation, and RCCC, in turn, has been working fon a project that is funded by SEPTA (the Susquehanna Estuary Public Transportation Authority).  They need to predict the voltage along a transit line.  Dr Malllity says that the situation can be predicted using the circuit below.

In this situation, SEPTA wants to do the following:

lThey want to supply the vehicle with 600v.
lThe 600v stations will be spaced as uniformly as possible along the line.
lWhen the vehicle is not right at a 600v station there will be current flowing through the rails to the train, and there will be a consequent voltage drop along the rails.
lThe resistance in the rails is modelled as R_Left and R_Right in the circuit above.
lThe resistance of the vehicle is modelled as shown above.
lThe rail resistance is .02W/mile
lThe vehicle has a resistance of 2W.

       SEPTA wants to know how far apart they can space the 600v stations and still keep the voltage across the vehicle at 550v or more.

        Mallilty - after extensive argument with Willy and Millie - now realizes that the circuit above is overly complex, and can be replaced by the equivalent circuit below.  He is also guessing that the worst case scenario is when the vehicle is half-way between the two 600 v stations, so your job is to determine the maximum distance the train can be from the station by determining the largest value that R_rail = R_left = R_right can have.