The infrastructure in much of Quebec has been suffering from under-investment for a number of decades. A particular problem is with the water systems, since when the pipes break, several streets can sometimes be closed at once. The small town where you live, St-Sulpice-de-Beatrice, has not escaped this problem. Your aunt works at city hall and obtained a small contract for you. You will work on the following situation.
The street plan and traffic flow (in cars/hour) into and out of downtown St-Sulpice-de-Beatrice are shown below.
Heavy rains recently overloaded the storm sewers and the resulting flood made three street sections impassable. The street closures were:
- 2nd Avenue between Rue De Maisonneuve and Rue Principale
- Rue Principale between 1st and 2nd Avenue
- Rue De Maisonneuve between 2nd and 3rd Avenue
The public works manager wants a thorough analysis of the situation. He wishes to know:
a) What the traffic flow pattern is like before any street closures.
b) Whether the remaining network will be able to handle the traffic flow if the planned street closures are carried out.
c) What the traffic flow patterns in the city will be like if only Rue Principale is repaired and, in particular, how many cars per hour will travel along the newly repaired section of road and in which direction.
d) The volume of traffic along the damaged section of Rue Principale before the flood, and whether repairing this road will cause the number of cars per hour to increase or decrease?
Note: To answer this part of the question, you may use the results of a traffic study carried out by a city hall employee, which observed that an average of 20 cars per hour drove from west to east along Rue De Maisonneuve between 1st and 2nd Avenues and 10 cars per hour drove from west to east along Rue De Maisonneuve between 2nd and 3rd Avenues.
Analyze the street system using systems of linear equations and provide the public works manager with the information he needs to know.