As part of The Fantastic Race, teams need to travel on buses from
city to city in the order Omicron to Pi to Rho to Sigma to Tau. Each
city has several different bus stations to choose from. Nate has created
the following map showing all the different bus routes between the five
cities, as well as the travel time, in minutes, for each. The different
bus stations within each city are labeled \(\text{A}\), \(\text{B}\), \(\text{C}\), etc.
Which route from Omicron to Tau gives the shortest total travel
time?
Omicron and Pi each have has \(4\) stations labelled \(\text{A}\), \(\text{B}\), \(\text{C}\), and \(\text{D}\).
Rho has \(3\) stations: \(\text{A}\), \(\text{B}\), and \(\text{C}\).
Sigma has \(5\) stations: \(\text{A}\), \(\text{B}\), \(\text{C}\), \(\text{D}\), and \(\text{E}\).
Tau has \(2\) stations: \(\text{A}\) and \(\text{B}\).
A table is provided below for each segment of the trip: Omicron to Pi, Pi to Rho, Rho to Sigma, and Sigma to Tau. The table gives the labels of the starting and ending stations, along with the time, for each route in the segment.
