How fast do the gray and black tanks fill

We carry 5 gal jugs of water for cooking and drinking and that helps. As others have stated, use less water, take less and shorter showers. DW hates this, she loves a long shower. I Cringe the entire time she is in there when we don't have full hookups. I explain the issue - she doesn't care. Apparently it's my issue. :-)

There is absolutely no way to tell how much water you will need. Habits are the big factor. At home I leave the faucet running while I wash my face and brush my teeth. Habits like that will run through the fresh water tank and overflow the gray water tank quickly.

When I camp and water is not available. I get by on about 3 gallons per day. Roughly 1 gallon for drinking, 1 gallon for dish washing and cooking, and the remaining gallon for a shower. I don't fall short but there is no wasted water in the processes.

Wife and I can go a week on the black tank, 5 days is the best so far on gray. We wash dishes outside in 2 tubs one to wash one to rinse and throw the water into the shrubs. ( I know the horror) Navy showers, never letting the water run while shaving or brushing teeth.

Comfortably (as water usage varies wildly based on.....use), 2 people, one week, navy shower every day and conserving water while doing dishes, you're up for at least 1 dump and refill of fresh and gray water.
Black tank will make it if you forego the preferred method of using "plenty of water" to wash down every #2 deposited.
Note when black tanks get full or near full, they generally start stinking if you drive any real distance (ie sloshing around for extended periods of time).

It will vary a lot.

2 showers/day plus dishes when on full hookup, we can easily fill the gray in a day.

If we are away from sewer, we can get 3-4 days on the gray without trying very hard.

If we are really careful a week is possible though usually, we would just use the bath house (or shower every other day).

Hot water uses more water to flush the cold water. We've used coffee pot hot water for dishes and "sponge baths" for long stays.

Depends on camping scenario, at least the black tank should go a week with just two users. If you are a seasoned RVer that actually does some RVing without hookups you could go 3-4 days (more for those who skip daily showers) on your 35gal grey tank, FW tank might be enough, again it depends on your knowledge of conservation when camping in a TT.

There is a learning curve for sure if you are new to the lifestyle, no biggie as it takes but a trip or two to figure out tank and battery capabilities. Speaking of batteries, hopefully you have at least some power hookups to restore consumed amphours, if not solar and/or genny will be needed since most battery banks will not last a week.

With moderate care and conservation and two people, I'd expect you should pretty easily get half the stay, perhaps a bit more. That's with taking navy showers and using real dishes, but being a bit careful not to waste water with either one and not letting the water run while brushing teeth, etc. The gray will fill up faster than the black, and with those tank sizes I'd guess the gray will be getting full about when the fresh water tank is getting towards empty.

Are you renting the trailer in-situ, or will you be pulling it? If the latter, you can simply pull it through the dump/refill station at the campground midweek; no need to buy a tote just for the trip.

If you take

If you use the campground facilities for showering and your fresh water for dish washing a couple of times a day then your grey tank should be OK for the week.

Black tank should be ok, but toilet flushes will use a good bit of fresh water, so you might use the campground toilet to conserve your fresh water.

You should always be using your tanks...with or without hookups. Keep the valves closed. Dump black when at least half full and use gray to flush the hose. With those size waste tanks, four days with conservative use.