anonymous
  • anonymous
Suppose you have a grassy field, and cows eat grass at a constant rate. Keep in mind, the grass keeps growing continuously. 48 cows can clear all the grass off the field in 90 days. 120 cows can clear all the grass off the field in 30 days. How many cows would be needed to clear all of the grass in 16 days? Round up to the nearest whole cow.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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experimentX
  • experimentX
48 cows can clear all the grass off the field in 90 days. 120 cows can clear all the grass off the field in 30 days. ??
anonymous
  • anonymous
yeah...
anonymous
  • anonymous
no contradiction. the grass keeps growing. \[initial + (grassgrowthrate * days) = (numcows * eatingrate) \] for simplification x + y * z = i * j in the context of this problem x + 30y = 120j x + 90y = 48j

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perl
  • perl
what is initial?
anonymous
  • anonymous
the amount of grass that the field had initially
experimentX
  • experimentX
yeah i figured out that.
perl
  • perl
so you set them equal to each other because you assumed they ate all the grass
anonymous
  • anonymous
I didn't assume, they said that they "cleared the field"
perl
  • perl
errr, that was given
perl
  • perl
so what exactly are you equating , what is your left side and right side
perl
  • perl
total grass grown = total grass eaten (over the days )
anonymous
  • anonymous
the initial grass plus the growth of the grass is equal to the grass that the cows ate in other words, when you subtract the total grass minus the grass eaten, it should equal zero, thus my equation.
perl
  • perl
ok but thats 2 equations in 3 unknowns
perl
  • perl
the grass is growing while they are eating
experimentX
  • experimentX
grass growth must be some function of days
anonymous
  • anonymous
i started this way, 1 cow eats an ammount of grass each day is m the grass grows by the amount n each day and if the initial is a then we get a+90n=48*90m a+30n=120*30 m
perl
  • perl
well you can subtract equation 1 from equation 2, that eliminates x the initial
anonymous
  • anonymous
by eliminating the initial i will find the relation between m and n
perl
  • perl
how did you get grass growth rate is 90 and 30 ?
perl
  • perl
nevermind
perl
  • perl
that was days
anonymous
  • anonymous
Yeah sritama I was actually just about to correct my equations to add the days on both sides.
anonymous
  • anonymous
yeah,i took the grass growth rate n/each day ... so it must b 90n and 30n
anonymous
  • anonymous
oh ok gingerkid 101
perl
  • perl
ginger can you redo your equation
perl
  • perl
i like your equation, its very logical :)
anonymous
  • anonymous
x + 30y = 120 * 30 * j x + 90y = 48 * 90 * j where x is in grass, y is in grass per day j is in grass per cow per day
perl
  • perl
yeah thats a little odd, grass per cow per day
perl
  • perl
how does that come out in units, grass/ (cow/day) or
anonymous
  • anonymous
probably it means the amount of grass taken by each cow per day
anonymous
  • anonymous
grass/(cow * day) or grass/cow/day it's all the same.
anonymous
  • anonymous
in other words, if you have a certain number of cows, you can multiply it by that number to get 30 cows * 1 grass/cowday = 30 grass/day is resulting from having 30 cows.
anonymous
  • anonymous
anyway the equations fully played out are... x + 30y = 3600j x + 90y = 4320j that's what I'm at right now.
perl
  • perl
ok now its linear algebra, one moment
perl
  • perl
x + 30y - 3600j=0 x + 90y- 4320j=0
perl
  • perl
I get x = 3240 j y = 12j j = j
perl
  • perl
actually we know we want 16 , so we have another equation
perl
  • perl
x + 30y = 3600j x + 90y = 4320j x + 16 y = 16 i * j
anonymous
  • anonymous
However, we also know that 8 additional cows are needed to balance the original proportion, which can possibly give us a 3rd equation? 8j - 60y = 0 or else the proportion would be even. therefore, we now have a 3 part system 8j - 60y = 0 x + 30y - 3600j=0 x + 90y- 4320j=0
perl
  • perl
how did you get 8 additional cows?
anonymous
  • anonymous
yeah,thats my question too
anonymous
  • anonymous
8 additional to 1/3 of 120. maybe I'm just talking out of my retricenow haha
anonymous
  • anonymous
I don't even know. meh, I never had to do anything like this and I took up to calc 3 haha
perl
  • perl
well this is a solid start
perl
  • perl
i got 12j = y , so 12 cows it takes to eat the grass grown in 1 day

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