Depending on which one is closer to your home and if you left your phone at home to avoid ping purposes; Then a potential suspect can say I was at the class over there because it is closer to my house. I arrived there at 4:50 am.
So it definitely would be a more solid alibi then the at home alone but my car was seen in town while I was heading home from the murder.
Plus going to the other class would be the best way to stay in the loop at 6am while the word is traveling around the fitness class. Jmo.
But this would mean that the perp would actually be a camper or affiliate.
So a regular hitman would most likely had just headed home. Jmo.