Quickest 7h 31min
There are 1 train company operating 3 routes - Texas Eagle, Cardinal, Capitol Limited, 3 flights and 3 buses from MIN to ALX. The cheapest train costs $254 and is 1d 6h 57min.
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There are 4 ways to travel from MIN to ALX. 4 trains, 3 flights, 3 buses and 1 by car are possible between the two areas. The by car from MIN to ALX is the cheapest. The flight from GGG to DCA is the fastest. The train operated by Amtrak running from MIN to ALX is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!