From Mountain Home it is, at least according to google maps:
I see. Your wording is confusing. How about do this.
"From Boise, take I-84 east for about 41 miles to Mountain Home. In Mountain Home, take the Exit 95 onto US-20 and head northeast towards Fairfield. It is about 100 miles from the exit off I-84 in Mountain Home to Carey."
The reason I bring this up is since I have traveled on the roads, and usually would suggest taking I-84 to US 75 instead. I guess Highway 20 is faster from Boise.