Quickest 7h 39min
There are 1 train company operating 3 routes - Southwest Chief, City Of New Orleans, Sunset Limited, 3 flights from GLP to HMD. The cheapest train costs $362 and is 1d 21h 13min.
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There are 3 ways to travel from GLP to HMD. 4 trains, 3 flights and 1 by car are possible between the two areas. The by car from GLP to HMD is the cheapest. The flight from FMN to MSY is the fastest. The train operated by Amtrak running from GLP to HMD 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!