Passage

Directions: Read the following and answer the question. Each of six persons - Madison, Lucas, Andrew, Faith, Marie and Amber - travels between exactly two localities, i.e. one locality is where the person lives and the other locality where he works from among six different localities - L1, L2, L3, L4, L5 and L6 - such that no two persons live in the same locality and no two persons work in the same locality. Further, no two persons travel between the same pair of localities. It is also known that the travel time, i.e. the time taken by a person to travel from home to workplace (calculated in minutes), is a distinct positive integer less than 8. The following information is known about home, workplace and travel time of six persons. (1) The workplace of Madison is the same as the home of Faith, but neither of these persons travels either from L2 or to L2. (2) The travel time of Marie is 2 minutes more than that of Andrew. (3) One of the persons lives in L1 and works in L6, with a travel time of three minutes. (4) The travel time of Amber, who works in L3, is less than 7 minutes, while the travel time of the person who lives in L3 is 2 minutes. (5) The travel time of Lucas, who lives in L5, is the average of the travel times of the persons who live in L4 and L6. (6) The person who works in L2 lives in L3, while Faith does not live in L6.

Find the average travel time taken by all the six persons.