A cyclist must reach a checkpoint that is 6 km east and 4 km north of her current position. She can ride along a straight east–west paved road at 30 km/h and then pedal across a grassy field at 10 km/h. She may leave the paved road at any point C located x km east of her starting point (where 0≤x≤6) and head straight to the checkpoint.
a. Express the total travel time T(x) (in hours) as a function of x. Clearly indicate the domain of T.
b. Find the value of x that minimizes T(x). Give your answer to two decimal places.