A man, who is in a rowboat 2 miles from the nearest point A on a straight shoreline, wishes to reach a house located at point B which is 6 miles further down the coast. He plans to row to point P that is between A and B. P is also x miles from the house. He will then walk the remainder of the distance to the house. Suppose he can row at the rate of 3mph. He can walk at the rate of 5mph. If T is the total time to reach the house, express T as a function of x.

[--------------------------6miles------------------------]

..........................................[----------- x ------------]

A_________________________P______________________B (house)

|......................................../

|2................................./

|m........................./

|i..................../

|l.............../

|e........./

|s...../

|./

.

(rowboat)