The only long distance passenger train system in the US is Amtrak, and as far as I know they don't go to South Dakota.
The closest station to South Dakota that I could find was Detroit Lakes, MN, and from Philadelphia it would take you around a day and a half to get there. (Most of the trains that would let you do it leave Philadelphia around noon, and get to Detroit Lakes about 2 in the morning on the second day following.)
It's worth noting that Detroit Lakes is not all that close to South Dakota; it's probably 75 miles or so northeast of the northeast corner of the state.
In the US, taking the train is rarely much cheaper than the lowest plane fares (21-day advance tickets), so you might want to look into alternative travel methods.
24 hours from Orlando to Philadelphia on the Amtrak train
9 hr
A flight from LAX to South Dakota takes about 3 hours. The distance between LAX and South Dakota is 1,238 miles or 1,993 kilometers.
5 hours and 39 minutes.
South Dakota is about 383 miles long (east to west) and 237 miles wide (north to south).
South Dakota is further north than North Carolina.
Yes, South Dakota has wetlands. Wetlands are also known as marshes, sloughs, swamps, bogs, and potholes. In South Dakota they are generally known as sloughs and may be dry for long periods of the year.
about 24 hours
Nebraska and South Dakota share a common border, so travel time would be as long as it takes someone to step across the state line.
Google Maps estimates the driiving time as 5 hours and 45 minutes.
16 hrs.
15 hours