From SLC, one could take I-15 to I-40 then cross over to UT24 to Hanksville, but it is definitely much longer of a trip. US-6 from Spanish Fork to I-40 is four lane for a good portion of the drive to Soldier Summit, and is 65mph the whole way except near Price.
I-15/I-40/UT-24 : approximately 369 miles
I-15/US-6/I-40/UT-24 : approximately 231 miles
There are plenty of other variations to these too if one wanted to mix it up even more.