The owner is asking for just 2 hours a day. There are some days where she might need me for the whole day, in which I would charge my day rate. So is there a particular formula on calculating hourly?
Agree with Walt.
If your schedule allows to spend 2 hours there, you may be able to earn some loyalty in the way of repeat business and referrals, by booking it as a drop in, and not adding a few more dollars, which is likely as much as you could.
It doesn't appear that you have a day care rate set up, but I'd guess it might be about $30-35 between your drop in rate (set at $20) & house sitting (set at $47).
I don't really care for pro-rating, the way our services are priced there's really no rhyme or reason. For petsitting for someone, I think I would be inclined to say my rate is the same whether 1 hour or (max time).
There isn't a standard I've ever seen for calculating an hourly rate for pet care. But using your house sitting rate as an example you charge less tha $2 an hour, now that's too low! I might suggest you use your drop-in rate for just 2 hours
My dog boarding rate is $25 per 24 hours, if they do a half day, I will adjust the rate before booking down to $12.50. Basically your rate for boarding should be for 24 hours and then divide your rate based on hours. For example, my recent stay was from Saturday 9am until Sunday 8pm, I asked for $25 plus additional $12.50 for the hours after the first 24 hours have passed. I have done this now with 3 different clients, one is a repeat and they did not seem to have a problem with it at all and left great reviews.