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Our RIR hens started at around 20-24 weeks. But I've had one that went almost 8 months before she layed an egg. Doesn't matter whether you have a rooster or not. Just like humans, chickens will ovulate (throw an egg out of the ovaries) whether there is a male around or not. Lucky for those of us who like eggs, chickens ovulate every 25 hours...humans only ovulate every 28 days.
To the OP, if I wanted 36 eggs per week consistently I would figure a 60-75% production rate (depending on the breed and time of year...most girls will drop to 40% production...some even 0%...during the winter, and mine give 85% Spring thru Fall).
6 hens at 60% = 25 eggs per week
8 hens at 60% = 34 eggs per week
10 hens at 60% = 42 eggs per week
6 hens at 75% = 32 eggs per week
8 hens at 75% = 42 eggs per week
My EE's were horrible last winter, dropping down to no eggs at all from 5 girls from early Dec until about theend of January when they slowly ramped back up to 75% in Feb. My 6 RIR's layed around 5 eggs per day all winter = 83%. So I've learned to choose my breeds carefully if I want our egg customers to be happy! I will be curious to see how our new sexlinks do this winter.
I currently have 3 delawares, 2 RIR, 2 barred rocks, and 4 EE's (11 hens total). We get 8-10 eggs per day...about 5 dozen per week right now during prime laying season.