Answer: Drum composters can produce finished compost in about 10 weeks. They are not considered "continuous use" so, you're right, at some point you will need to stop adding new material to the composter. A second composter would be the easy answer to your quandry. Or, burying the kitchen waste in the soil, with the intention of digging it up and adding it to your composter at a later date might work for you. You might also consider building a holding bin out of hardware cloth while your tumbler is occupied. Hope these suggestions help.
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