The Turkey Problem:
If a family and a half (1 ½ family) can eat a turkey and a half (1 ½ turkey) in a day and a half (1 ½ day),
how many families can eat six turkeys in six days?
Haha sorry its not corgi related but i am wondering if anyone can figure this one out!
Comment
Thanks For The Explanation John!
Mr. Wolf, this smart-ass was about to type in "6" before seeing your nice long post on the subject. I made a point to just skip to the end to make sure I wouldn't be embarrassing anyone with my simple answer. Seeing that your formula had already made allowances for the smart-ass in the back of the room, I feel comfortable in my initial response. 6.
The key is to note that this is the same as asking how many families are needed to eat 1 turkey in 1 day (6 turkeys/6 days = 1 t/d). 1.5 turkeys in 1.5 days = 1.5 t / 1.5 d = 1 t/d i.e., 1 turkey per day.
It takes 1.5 families to do that, so the rate is 1 turkey per day per 1.5 families, or 2/3 = 0.667 turkeys per family-day:
1 t/d divided by 1.5 families = 0.67 t/f-d. 1 family can eat 0.67 (2/3) turkeys in one day.
Let R = consumption rate, 2/3 turkeys per family-day = 0.67 t/f-d
Let F = # of families (we want to solve for this).
Let D = # of days (this factor disappears, since D=1, see above).
Let T = # of turkeys eaten (this factor likewise disappears, since T=1, see above).
T = R x F x D = R x F
1t = 0.67t/f-d x F x 1d (note that the units "t" for "turkeys" and "d" for "days" both cancel out):
1 = 0.67/f x F
{kids: to solve for F, divide each side of the equation by 0.67t/f-d; you can always multiply or divide both sides of an equation by anything you want without changing it: Identity Propeyrt of Multiplication: if a=b, ax = bx}
1 / 0.67/f = F
1.5f = F
So it takes 1.5 families minimum to eat 1 turkey in one day. They do that 6 days in a row.
Note the hidden assumption that the rate remains constant! Our unexamined assumptions are what get us into trouble. Even a corgi might be kinda stuffed by, say, Day 4. R might diminish, increasing D and/or F. Might need more time and families.
Note the hidden assumption that corgis are absent. That would change everything.
<smartass kid in back row raises hand>
"Hey, Mr. Wolff, wouldn't it be a lot easier to simply note that if 1.5 families can eat 1.5 turkeys in 1.5 days, they can eat 1 turkey in 1 day, and thus 6 turkeys in 6 days?"
doh.
Mr. Marko taught me how to do this in 9th grade Algebra I. He ran off with one of his teenaged students.
Haha. I should e-mail my math teacher that! I will be like, wouldnt they be sick of turkey by then? I bet my Daisy wouldnt! No respectable corgi would. lol
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