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If a hen and a half lays an egg and a half in day and a half, how many eggs will six hens lay in nine days?

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closed as off-topic by boboquack, Wen1now, Beastly Gerbil, Mithrandir, Rand al'Thor Oct 22 '17 at 15:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – boboquack, Wen1now, Beastly Gerbil, Mithrandir, Rand al'Thor
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  • $\begingroup$ Half a hen can't lay an egg- dead hen. Half an egg would an awful mess. $\endgroup$ – user2617804 Oct 22 '17 at 9:18
  • $\begingroup$ “If one and a half chickens lay one and a half eggs in one and a half days, how many eggs will nine chickens lay in nine days?” - Isaac Asimov, Escape, I, Robot. Look familiar? $\endgroup$ – Wen1now Oct 22 '17 at 10:28
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Assuming there's no "gotchas!" with things like how half an egg could be laid etc. the answer is:

36 eggs

Reasoning:

If 1.5 hens lay 1.5 eggs in 1.5 days, then 1 hen will lay 1 egg in 1.5 days. 9 days is 6x1.5 day periods, so the 6 hens will each lay 6 eggs, for a total of 36 eggs.

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x hens lay y eggs in z days.

x hens lay $y\times\dfrac{9}{z}$ eggs in 9 days.

6 hens lay $\dfrac{6}{x}\times y\times\dfrac{9}{z}$ eggs in 9 days.

In this case $x=y=z=\dfrac32$, so:

$$6\cdot\frac23\times\frac32\times9\cdot\frac23=4\times\frac32\times6=36\,\text{eggs}$$

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    $\begingroup$ I eggspected for eggsample the half a hen would be eggspired then it shell lay duck eggs. $\endgroup$ – Tom Oct 22 '17 at 8:37
  • $\begingroup$ $\pi$ hens lay $e$ eggs in $\phi$ days... $\endgroup$ – JonMark Perry Oct 22 '17 at 8:59
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They will lay:

36 eggs

Because:

Hens   Eggs   Time
1.5    1.5    1.5
6      6      1.5
6      36     9

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