Laying Eggs Better by HalfDate: 12/05/2001 at 08:47:39 From: Kenneth Klein Subject: Puzzle Ratio If a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half? Date: 12/05/2001 at 12:55:49 From: Doctor Peterson Subject: Re: Puzzle Ratio Hi. Kenneth. I think this wins the prize as the most complicated version I've seen of this old puzzle. You can find other versions by searching our site for the phrase and a half (that exact phrase): A Hen and a Half http://mathforum.org/dr.math/problems/chase9.23.98.html A Chicken and a Half?! http://mathforum.org/dr.math/problems/green5.7.97.html For a quick solution to your version, we can start by finding the laying rate in eggs per hen-day: 1.5 eggs ------------------- = 2/3 eggs/hen-day 1.5 hens * 1.5 days Now a hen that is "better by half" will lay 1.5 times as many, or 1 egg per hen-day. A score and a half is 1.5*20 = 30, and half of that is 15. (I could also read that phrase as "1.5 times half a score," but I would get the same answer.) A week and a half is 1.5 * 7 days, or 10.5 days. I have to solve a rate equation of the form Eggs = Rate * Hens * Days for the number of hens: Eggs 15 eggs 15 Hens = --------- = ------------------------- = ---- hens = 1 3/7 hens Rate*Days 1 egg/hen-day * 10.5 days 10.5 Finally, what in the world does "how many and a half" mean? I think we have to solve 1.5 X = 10/7 which gives X = 20/21 hens. After all that work, the problem wasn't designed to give us a whole number answer?? Ahh - maybe "half a score and a half" was meant to be 10.5. Then we can replace 15 eggs with 10.5 eggs, and the first calculation just gives 1 hen. And in that case, "how many and a half" probably means X + 1/2 = 1 so the answer is half a hen: "Half a hen and a half (one hen) that lay better by half (one egg per hen day) will lay half a score and a half (10.5 eggs) in a week and a half (10.5 days)." No wonder mathematicians don't speak like this! Our goal is to communicate rather than to confuse. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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