Hi,
Let me first say that I started reading SD only recently, and can’t believe how late to the party I am.
While the solution in the column is correct, we can get away without juggling fractions.
1.5 hens lay 1.5 eggs in 1.5 days
So the same number of eggs in the same number of days (are laid by 1.5 hens)
How many hens lay 6 eggs in 6 days? 1.5
How many hens lay x eggs in x days? 1.5
I think the tricky part is actually that each of first 2 “one and a half”'s would, by themselves be greater than 1/day. (more eggs per chicken, or more chickens with one egg), but the “day and a half” actually reduces the rate. IF rate=total/time then total+n is a higher rate, but time+n is a lower rate.
If your talking about rates of production, then it is certainly sensible to talk about producing 1.5 eggs per day. All that means is that, on average, it takes 2 days to lay 3 eggs. It does not mean that the egg takes ~ 16 hrs to pass through the cloaca.
Furthermore, if you are speaking about rates, then it is acceptable to vary the number of chickens involved for the comparison. One can look at per each chicken, or per 2 chickens, or per a dozen chickens.
What makes it sound funny is when you start taking those statistical quantities and then preface your question with a non-integer number of chickens. That sounds funny. “How does half a chicken do anything?” But realize it’s just a rearrangement of a rate statement. As a rate statement, it can be mathematically converted to a different rate base.
A half a chicken can lay half an egg, no problem. It just has to be attached to another half-chicken, which simultaneously lays the other half of the egg.
Kidding aside, the joke is structured so that all the numerical values match; “1.5 hens lay 1.5 eggs in 1.5 days” is mathematically equivalent to “1 hen lays 2 eggs in 3 days”. but the fractional form encourages the patsy to think the pattern is for all the values to match, so when you ask “How many days does it take for 6 hens to lay 6 eggs?” he’s tempted to quickly (and incorrectly) answers 6.
The fact that fractions are involved makes the temptation to follow a simpler pattern more alluring. I don’t think as many people would be fooled if you premised “1 hen lays 1 egg in 1 day”.
I agree. Half hens don’t lay eggs. So one hen is producing one egg and half an egg in a day and a half. Since we’re looking for six eggs, and not any half eggs, it would take two hens to lay six eggs in six days, plus you get two extra eggs and eight half eggs to boot.