I drove straight through from Steamboat Springs to San Marcos once after my daughter's softball tournament. Used I-70 to I-15. It took 18 hours

. Now that we live in CO, we've driven to Vegas a few times(12 hours) from Monument. I think you'll do better because we have a young daughter and sometimes a dog, so we stop more than most.
I-15 has some stretches without services, but if you fill in St George or Cedar City, you should have more than enough fuel to get to Richfield. Beaver is somewhere between also.
I think I-70 is one of the most scenic highways I've ever driven. Have fun and be safe.