# Ooh, me Farmers!

Mathurine
Posers and Puzzles 09 Feb '07 19:15
1. Mathurine
sorozatgyilkos
09 Feb '07 19:15
Farmer Giles owns a piece of grassland and three animals: a cow, a goat, and a goose. He discovered the following:

When the cow and the goat graze on the field together, there is no more grass after 45 days.

When the cow and the goose graze on the field together, there is no more grass after 60 days.

When the cow grazes on the field alone, there is no more grass after 90 days.

When the goat and the goose graze on the field together, there is no more grass after 90 days also.

For how long can the three animals graze on the field together?
2. sonhouse
Fast and Curious
09 Feb '07 19:37
Originally posted by Mathurine
Farmer Giles owns a piece of grassland and three animals: a cow, a goat, and a goose. He discovered the following:

When the cow and the goat graze on the field together, there is no more grass after 45 days.

When the cow and the goose graze on the field together, there is no more grass after 60 days.

When the cow grazes on the field alone, ther ...[text shortened]... s after 90 days also.

[b]For how long can the three animals graze on the field together?
[/b]
Solve like parallel resistances, (1/x+1/y+1/z) ^-1 So the the grass lasts 90 days from the cow, 90 days from the goat (for two resistors in parallel, R1*R2/R1+R2, 90X90/180=45.) and 180 days for the goose so its 1/90+1/90+1/180 which is .0277777 and change, invert that and you get 36 days.
3. Mathurine
sorozatgyilkos
09 Feb '07 19:40
Brilliant!
4. sonhouse
Fast and Curious
09 Feb '07 19:44
Originally posted by Mathurine
Brilliant!
5. 09 Feb '07 19:47
My only problem with this is that the cow takes 90 days, the goat takes 90 days, and the goose takes 180 days alone to eat all of the grass. But according to your problem with the goat and the goose on the land, the land is empty in 90 days but if the goat eats it in 90 alone, then with the goose it HAS to be less than 90. According to ab/a+b. It should be 60 days for them both to eat it.
6. sonhouse
Fast and Curious
09 Feb '07 19:552 edits
Originally posted by MrVandalay
My only problem with this is that the cow takes 90 days, the goat takes 90 days, and the goose takes 180 days alone to eat all of the grass. But according to your problem with the goat and the goose on the land, the land is empty in 90 days but if the goat eats it in 90 alone, then with the goose it HAS to be less than 90. According to ab/a+b. It should be 60 days for them both to eat it.
Cow + goose=60 days. So invert that. =.01666666....
Cow = 90 days. Invert that, =.011111111....
Invert 180=.0055555555...+.011111111=.01666666 which inverted gives us our 60 days.
But that makes statement 4 invalid. So statement 4 should read 60 days. I see what you mean.
7. Mathurine
sorozatgyilkos
09 Feb '07 22:28
Originally posted by sonhouse
Cow + goose=60 days. So invert that. =.01666666....
Cow = 90 days. Invert that, =.011111111....
Invert 180=.0055555555...+.011111111=.01666666 which inverted gives us our 60 days.
But that makes statement 4 invalid. So statement 4 should read 60 days. I see what you mean.
oops! 😳
8. sonhouse
Fast and Curious
09 Feb '07 22:39
Originally posted by Mathurine
oops! 😳
Funny, I just used the first three, didn't pay attention to statement 4.
9. AThousandYoung
09 Feb '07 23:502 edits
Let G = goat's rate of feeding in grass/day
B = goose's rate
C = cow's rate
F = total amount of grass

I started working on statements 1 and 3, but the problem came in 2 and 4:

1. 45C + 45G = F
2. 60C + 60B = F
3. 90C = F
4. 90G + 90B = F

45C + 45G = 90C
45G = 45C
C = G

60C + 60B = 90G + 90B
60G = 90G + 30B
-30G = 30B

Impossible! The problem is paradoxical. Unless of course the Goose can eat Goat turds, or vice versa.

I wonder if this is solveable assuming that turds can increase the "grass" supply?
10. 10 Feb '07 13:03
Originally posted by AThousandYoung
Let G = goat's rate of feeding in grass/day
B = goose's rate
C = cow's rate
F = total amount of grass

I started working on statements 1 and 3, but the problem came in 2 and 4:

1. 45C + 45G = F
2. 60C + 60B = F
3. 90C = F
4. 90G + 90B = F

45C + 45G = 90C
45G = 45C
C = G

60C + 60B = 90G + 90B
60G = 90G + 30B
-30G = 30B

Impos ...[text shortened]... ersa.

I wonder if this is solveable assuming that turds can increase the "grass" supply?
Which either the goat or goose can eat reducing the amount of grass being produced.
11. sonhouse
Fast and Curious
10 Feb '07 18:31
Originally posted by AThousandYoung
Let G = goat's rate of feeding in grass/day
B = goose's rate
C = cow's rate
F = total amount of grass

I started working on statements 1 and 3, but the problem came in 2 and 4:

1. 45C + 45G = F
2. 60C + 60B = F
3. 90C = F
4. 90G + 90B = F

45C + 45G = 90C
45G = 45C
C = G

60C + 60B = 90G + 90B
60G = 90G + 30B
-30G = 30B

Impos ...[text shortened]... ersa.

I wonder if this is solveable assuming that turds can increase the "grass" supply?
We already figured out he made a mistake on statement 4, it should have read 60 days not 90. That removes the impossibilities.
12. 11 Feb '07 01:26
Originally posted by AThousandYoung
Let G = goat's rate of feeding in grass/day
B = goose's rate
C = cow's rate
F = total amount of grass

1. 45C + 45G = F
2. 60C + 60B = F
3. 90C = F
4. 90G + 90B = F
[snip]
I wonder if this is solveable assuming that turds can increase the "grass" supply?
I am having real problems with this one.
The grass supply is increasing each day - it's growing!
Let's take the scenario of the cow eating C per day.
There is F amount of grass initially.
With no animals involved let's have a growing rate of x, where x is the amount of new growth each day. So if there is F grass today then tomorrow there will be F*x. If there is F/2 grass today then tomorrow there will be (F/2)*x.
For the cow scenario you would get (F-C)*x after one day, ((F-C)*x-C)*x after two days ... etc. After doing this 90 times you would have zero grass left.
Can anyone help?
13. sonhouse
Fast and Curious
11 Feb '07 15:06
Originally posted by Diapason
I am having real problems with this one.
The grass supply [b]is
increasing each day - it's growing!
Let's take the scenario of the cow eating C per day.
There is F amount of grass initially.
With no animals involved let's have a growing rate of x, where x is the amount of new growth each day. So if there is F grass today then tomorrow there will ...[text shortened]... days ... etc. After doing this 90 times you would have zero grass left.
Can anyone help?[/b]
Interesting take on the problem. I think the original problem as stated ignored a replacement factor, making it a flow problem, like the amount of flow of the grass into the guts of the individual animals. I think he assumes there is no growth of the grass in that time and to get more you need to reseed. He could have also factored in the growth rate so the farmer knows how long the grass lasts INCLUDING the new growth.
14. 11 Feb '07 17:11
Originally posted by sonhouse
Interesting take on the problem. I think the original problem as stated ignored a replacement factor, making it a flow problem, like the amount of flow of the grass into the guts of the individual animals. I think he assumes there is no growth of the grass in that time and to get more you need to reseed. He could have also factored in the growth rate so the farmer knows how long the grass lasts INCLUDING the new growth.
Fair enough. If you assume no grass-growth then it's a parallel resister problem. I can cope with that!