Amtrak Acela Express operates a train from Columbia to Philadelphia hourly. Tickets cost $80 - $220 and the journey takes 1 h 13 min. Alternatively, American Airlines flies from Columbia to Philadelphia 3 times a day.
From Columbia taxi to BWI Marshall Airport Amtrak then train to Philadelphia 30th Street Station Amtrak. 1 h 32 min $255. From Columbia drive to Philadelphia. 2 h 10 min $14. From Columbia Mall line 501 bus to Baltimore airport, fly to Philadelphia airport, then train to Philadelphia. 3 h 43 min $370.