Quickest 7h 25min
There are 3 buses1 train company operating 2 routes - Texas Eagle, California Zephyr, and 3 flights from Austin to Logan. The cheapest train costs $404 and is 2d 2h 50min.
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There are 4 ways to travel from Austin to Logan. 3 buses, 4 trains, 3 flights and 1 by car are possible between the two areas. The by car from Austin to Logan is the cheapest. The flight from AUS to PVU is the fastest. The train operated by Amtrak running from AUS to SLC 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!