Amy,
I'd like to have more confidence in telling you how much chlorine to use and whether it will work for the 10 days. Are you leaving right away or do you have time to do an experiment? If you have time, then the following would give us enough info to figure this out.
1) We definitely need your CYA level so get that measured (do you have Ben's test kit?). This will tell us the minimum final chlorine level you can have on day 10.
2) In the evening (or any time not during the heat of the day when the sun is on the pool) test your chlorine level and add enough chlorine to raise the level to at least 5 ppm, though 10 would be even better (assuming you are using a FAS-DPD drop chlorine test kit; otherwise, 5 should probably be your starting point). Then, cover your pool. If your pump is not normally running at this time, turn it on manually until step 3.
3) After an hour, measure the chlorine level in your pool. This is your starting chlorine level. You can turn off your pump back to its normal automatic mode if its normally off at this time.
4) After 24 hours, measure the chlorine level in your pool. The ratio of this amount over the amount found in step 3 gives your retention ratio. If you want, you can continue the experiment for another 24 hours (don't add any more chlorine) since that will give you more accuracy. Three days would be even better. At the end of your experiment, you can uncover your pool during the day which will breakdown a lot of the chlorine so you'll be able to swim (if you want).
The formula for figuring out how much chlorine to add is as follows.
Starting Chlorine = (Ending Chlorine) / (Retention Ratio)^10
The "^10" means raising the Retention Ratio to the 10th power (the y^x function on the calculator).
Hopefully, the ratio of chlorine from day 2 to day 1 is about the same as the ratio from day 3 to day 2. If so, then we can be reasonably sure at our prediction. If the drop is very slow, then we can use the drop over 2 or 3 days via "Retention Ratio = ( (FC at Day N)/(FC at Day 1) )^(1/(N-1))
A simple alternative is to dump a whole lot of chlorine -- 30 ppm -- as if you were shocking the pool, but because it is kept covered, it won't really be shocked well. Your cover may not like this high chlorine level, but it will just be for 10 days (no guarantees).
Richard

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). I'm sure the thing won't last long anyway, I'm not too worried about it losing life. It's pretty thin and so I guess it probably wouldn't keep out sun anyway, I'll have to pull it out and see but I would imagine it's main purpose is keeping debris out of the pool.
, I can't really tell.....I live way out in the sticks and it is very inconvenient for any of my friends to drive all the way out here to mess with the pool - I would never ask them to. I have many pets that are going to be graciously well cared-for by my immediate neighbors, I don't want to dump the pool on them as well. That care and time is taken with my animals is much more important to me than overwhelming the caretakers with "a very complex and intricate" additional burden - which I myself don't even fully understand.
, but that may be my only option. I do have time before I leave and I will try your outline Chem Geek Richard (sincere thanks for the time you put into posting your experiment!