Have been asked to take care of two dogs in their home
I charge $5 if I am to stay in their home and care for their dog(s). I do give a discount on the second dog, the same as if they were boarding with me, for several reasons. Like Deb, if I'm to stay in their home, I have to be away from my home and change my routine, so I feel it's financially reasonable to charge more. And it depends on how far away they live. If they are close to my home I might give a discount because it cuts down on travel time. I haven't had that happen yet, though. My one housesitting stay was about 15 miles away from my house.
If they don't have Internet connections it's a definite no, because I need to stay connected to my friends/family and I have a part time job that is online.
Be sure and have a thorough discussion of what's expected of you and what they will be providing. For example, will they stock the kitchen with food and drink or do you bring your own? Will they provide towels, etc, for your bath/shower? Are you allowed to use their pool? Are there community facilities and can you use them? My client had a community pool, and she left me her access card. If you provide your own food, how close is the grocery or drug store? Be sure and ask how appliances operate (voice of experience here).
That is what I consider Travel or House Sitting. Each pet parent and their pet(s) are different, so you'll definitely want to discuss everything before booking. This is a premium service that I charge more for. If the pet parent wants me to stay there at all times, it requires me to pack change of clothes/toiletries, food/beverage, and anything else I may want to read or do, and driving there/back, in addition to declining other booking requests, even if there is just a small overlap.