A goat can eat all the grass in a farmer's field in 12 days, whereas a cow can finish it in 15 days and a horse in 20 days. How long will it take before all the grass is eaten if all three animals graze in the field?
please show work so i can understand.. thank you very much.
2007-11-01 12:02:25 · 5 answers · asked by little jimmy 2 in Education & Reference ➔ Homework Help
Hello again, Jimmy! This one's trickier than the other ones.
OK, so a goat eats everything in 12 days. So the goat's rate of eating grass is x/12 (if you let x be how much grass there is) Similarly, the cow's rate of eating is x/15 and the horse is x/20. (Think of it this way, when the question says eaten "in 12 days" that means "over a time of 12 days" or really "over 12" -- and that's a fraction.
If they all eat together, then the grass is getting eaten at the rate of all them working together:
x/12 + x/15 + x/20
get some common denominators. . .
5x/60 + 4x/60 +3x/60
So the new combined rate of eating the grass is 12x/60 (meaning, 12 lawns could get eaten over a time of 60 days) which can be reduced to x/5.
That means, the lawn will now get eaten "over 5 days" or "in 5 days." So it takes 5 days.
2007-11-01 12:11:26 · answer #1 · answered by .. 4 · 1⤊ 0⤋
The above anwser is one way of looking at it, however, I beleive I have an easier method. If the goat can it all of the grass in 12 days that means he can eat 1/12 or 8.33 percent of grass in one day. The cow can eat 1/15 or 6.67% and the horse 1/20 or 5%.
If you add all those perecents (8.33+6.67+5) you would get 20%. The 20% represent how much grass they will eat in one day. And if you want it all eaten (100%), you would just divide 100/20 which would equal 5 days.
2007-11-01 12:17:25 · answer #2 · answered by Avenger0786 2 · 1⤊ 0⤋
12 goat = 1 field per day (fpd)
15 cow = 1 fpd
20 horse = 1 fpd
1 goat eats at the rate of 1/12 fpd
1 cow eats at the rate of 1/15 fpd
1 horse eats at rate of 1/20 fpd
rate of consumption = 1/12 + 1/15 + 1/20 fpd
thats 5/60 + 4/60 + 3/60 = 12/60 fpd
= 1/5 of a field a day.
I make it 5 days
2007-11-01 12:20:52 · answer #3 · answered by philip_jones2003 5 · 0⤊ 0⤋
I don't know how you can answer the questions without more information. If it has to be answered I would try to find out the speed at which they all eat. For Example: 10ft squared per hour. So I would make up a number to the size of the field and figure out the speeds from there. Then somehow I would find the answer putting the numbers together. This would probably get you a wrong answer for sure but I've never answered a question like that so don't take my advice. By the way, Sarah Rains answer seems promising and smart and it makes sense so I would go with hers for sure.
2007-11-01 12:13:43 · answer #4 · answered by ldr0592 2 · 0⤊ 0⤋
If there is a fire, then you cannot accurately compute this question.
A terrible earthquake would likewise complicate the formula.
Constant rains may cause slides, thus covering the hilly areas with mud.
The question is unanswerable until such are factored in. I suggest you rephrase the question, so we may help you.
.
2007-11-01 12:05:45 · answer #5 · answered by Anonymous · 0⤊ 0⤋