Kathleen Taylor, a student at Tech, is planning to visit her sister, Lindsey, who is living in Toulouse, France, over the summer break. She is going to fly from Dulles Airport in Washington to Charles de Gaulle Airport in Paris, and because of the time changes, this travel will take a full day. In Paris, Kathleen is going to spend 2 nights and 1 full day before taking the train to Toulouse. Kathleen has never been to Paris, so she wants to spend her 1 day there seeing as many of the famous attractions as she can, including the Eiffel Tower, the Louvre, Notre Dame Cathedral, the Arch de Triumph, the Pantheon, and the Palace at Versailles. She plans to stay at a youth hostel very near Sacre Coeur in Montmartre and from there use the Paris Metro to visit as many of the sites as she can in a day. She has downloaded a detailed Metro map from the French rail Web site at www.ratp.fr and has discovered that the Metro system is huge, with almost 250 stations and 14 lines throughout Paris.

There’s no question that Kathleen can get to all the sites by the Metro, but she is concerned about her limited time frame and her ability to get from location to location quickly. She has determined the following information regarding the average times (in minutes) between stations for each line:

                                    

She’s also guessing that the subway stops about 1 minute at each station. If she has to change lines, she assumes it will take her at least 5 minutes. She plans to leave early in the morning, when the sites open, and she has no specific time she must be back to the hostel.

Kathleen, a business student, would like to use some of kind of logical, systematic approach to help her plan her movement using the Metro around the city to the different sites. Help Kathleen develop a route around the city to each of the sites she wants to see, starting from her youth hostel in Montmartre, for the day she’ll be in Paris. Do you think she’ll be able to see all the sites she wants to see?