A data point, probably not very useful:
My cat's vet charges $15 a day. But they put them in those stainless steel cages in the back (like what you'd see at a humane society). And my cat hates the vet's office because he only goes there for his rabies shot every three years (healthy indoor cat).
So I pay $15 a day to my youngest offspring if they're available. The rule is they get paid the daily rate if they do anything for the cat - food, water, litter, training, playing. Cat is happier to stay at home and kid is happy with that rate of pay considering the cat needs maybe 5 minutes of care per day.
If I'm gone for about four or five days or less, and kid isn't available, then I just prep the cat situation before I leave and he is on his own. He's a bit lonely when I'm gone, but he survives and is probably unknowingly very glad not to have gone to the vet.
If I had to use a non-offspring, I'd expect to pay more, because they'd have transportation time to/from my place. If they stayed at my place, that might be a benefit or a burden to them, so I'd consider that in the pay also.
I haven't yet had to face the situation of being gone too long and kid not available. There's a local "cat hotel" which is more like $50 to $60 a day. I've considered that for this kind of situation.