Average person = ~200
Seriously, though, countries with functioning infrastructure have trains that go nearly everywhere, or at least close enough you can walk or bicycle the rest of the way.
The real problem is the suburbs.
That said, rural college towns can have pretty awesome bus systems that run all year, even during subzero temperatures, and they can also have bike paths that go mostly everywhere, which are usable for nine months of the year. Because mine has all that. I'm sorry yours doesn't; but obviously, there is room for improvement, which is exactly my point.
Oh you mean those countries without poverty, unemployment, corruption that built pollution free cities where everybody is happy?
Seriously.
First not everybody can or wants to use a bicycle.
Additionally you can't possibly hope to give access train to every part of the "country", that would be 1/extremely expensive 2/extremely uncomfortable for people living close to lines.
You need a density threshold. You can't have a bus line for two people once a week. You can see the density threshold problem in action in the USA.
Lastly comes the problem of service time. It's impossible to offer 24/24 7/7 service except for the most busy lines.
But perhaps you're willing to put 50% of the GDP into public transportation?
I live in a city with outstanding public transportation (Paris). Metro, buses, mini-buses, taxis, bicycle rental, you name it.
Yet, if you have several appointments within the same day in the city, it's not doable by public transportation because of the waiting and walking time that adds up extremely quickly.
If you go out to see friends that live outside the city, it's not doable to come back after midnight.
If you want to visit someone that lives outside the city, it might take a lot of time to use public transportation.
You're dreaming if you believe you can build a public transportation system that solves all transportation problems for everybody. If your system is good, you'll help people to go to and back from work and move around the city for a decent price.
But you'll always need individual transportation (In my case I ride a motorcycle. It saves me a lot of time and headaches and it's just damn cool and fun!).
Welcome to the real world, where things are difficult.