The flight departs at 9:45 am at Taoyuan International Airport, and you live in Tainan. As a

rule, you have to get there 2-3 hours before flight departure. The distance between Tainan and TIA is around 270 km. If you take the earliest Taiwan High Speed Rail at Tainan in the morning, you will get to Taoyuan Station at 8:16 am. It takes another 30-minute transfer to TIA. So, it will be around 9 am by the time you have your check-in. I would say such arrangement would be too risky. Unless you want to stay at Taoyuan one day before the departure, the only choice seems to be by public bus transportation or by private car very early in the morning. And our choice was by car.
It will take around 3 hours (plus 30 minutes for the local) to get to TIA if the average driving speed is 90 km per hour. You want to follow the

rule, arriving the airport 2 hours before the departure. So, you have to hit the road not later than 4: 15 am. This means that you'd better get up at around 3:45 am. And this is what we planed for today's schedule.
What about the cost for the scenario of choice? Give you a brief quiz.
Before heading out, I filled up the fuel. On the highway to TIA, I bought a toll booklet (10 tickets) for NT$400. Note that I got two tickets left in my car before I got on the highway. Now, as we had planned, we arrived at TIA around 7:30 am. I helped Michelle check in at the service counter, saw her off, and drove back home

again. As I checked my fuel meter, I thought I'd better refill the fuel before heading back home. I did refill up and the receipt shows NT$749 for the fuel. When I got exit at Tainan, I found I run out all my toll tickets. Calculate the overall cost of fuel and tickets for this mission.
What's your number? You should come up with a number, NT$1978.
When I drove on the highway, I figured out this number around NT$2000 for sending Michelle from Tainan to TIA by car. Since I already paid for this amount of money, why not paying a surprise visit at any famous scenic spot along the highway? So, I stopped by at San-yi, a town of sculpture, where I had my brief lunch (NT$90), talked to a sculptor and visited the sculpture

museum (NT$80). I made another stop-by at my hometown, Ansiliao, where I greeted to my parents and took some photos as well.
It looks like I have made the best use of today.