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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.
 2 years ago
 2 years ago
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.
 2 years ago
 2 years ago

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experimentXBest ResponseYou've already chosen the best response.0
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. ??
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
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
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
the amount of grass that the field had initially
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
yeah i figured out that.
 2 years ago

perlBest ResponseYou've already chosen the best response.0
so you set them equal to each other because you assumed they ate all the grass
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
I didn't assume, they said that they "cleared the field"
 2 years ago

perlBest ResponseYou've already chosen the best response.0
so what exactly are you equating , what is your left side and right side
 2 years ago

perlBest ResponseYou've already chosen the best response.0
total grass grown = total grass eaten (over the days )
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
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.
 2 years ago

perlBest ResponseYou've already chosen the best response.0
ok but thats 2 equations in 3 unknowns
 2 years ago

perlBest ResponseYou've already chosen the best response.0
the grass is growing while they are eating
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
grass growth must be some function of days
 2 years ago

sritamaBest ResponseYou've already chosen the best response.0
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
 2 years ago

perlBest ResponseYou've already chosen the best response.0
well you can subtract equation 1 from equation 2, that eliminates x the initial
 2 years ago

sritamaBest ResponseYou've already chosen the best response.0
by eliminating the initial i will find the relation between m and n
 2 years ago

perlBest ResponseYou've already chosen the best response.0
how did you get grass growth rate is 90 and 30 ?
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
Yeah sritama I was actually just about to correct my equations to add the days on both sides.
 2 years ago

sritamaBest ResponseYou've already chosen the best response.0
yeah,i took the grass growth rate n/each day ... so it must b 90n and 30n
 2 years ago

perlBest ResponseYou've already chosen the best response.0
ginger can you redo your equation
 2 years ago

perlBest ResponseYou've already chosen the best response.0
i like your equation, its very logical :)
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
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
 2 years ago

perlBest ResponseYou've already chosen the best response.0
yeah thats a little odd, grass per cow per day
 2 years ago

perlBest ResponseYou've already chosen the best response.0
how does that come out in units, grass/ (cow/day) or
 2 years ago

sritamaBest ResponseYou've already chosen the best response.0
probably it means the amount of grass taken by each cow per day
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
grass/(cow * day) or grass/cow/day it's all the same.
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
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.
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
anyway the equations fully played out are... x + 30y = 3600j x + 90y = 4320j that's what I'm at right now.
 2 years ago

perlBest ResponseYou've already chosen the best response.0
ok now its linear algebra, one moment
 2 years ago

perlBest ResponseYou've already chosen the best response.0
x + 30y  3600j=0 x + 90y 4320j=0
 2 years ago

perlBest ResponseYou've already chosen the best response.0
I get x = 3240 j y = 12j j = j
 2 years ago

perlBest ResponseYou've already chosen the best response.0
actually we know we want 16 , so we have another equation
 2 years ago

perlBest ResponseYou've already chosen the best response.0
x + 30y = 3600j x + 90y = 4320j x + 16 y = 16 i * j
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
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
 2 years ago

perlBest ResponseYou've already chosen the best response.0
how did you get 8 additional cows?
 2 years ago

sritamaBest ResponseYou've already chosen the best response.0
yeah,thats my question too
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
8 additional to 1/3 of 120. maybe I'm just talking out of my retricenow haha
 2 years ago

gingerkid101Best ResponseYou've already chosen the best response.0
I don't even know. meh, I never had to do anything like this and I took up to calc 3 haha
 2 years ago

perlBest ResponseYou've already chosen the best response.0
well this is a solid start
 2 years ago

perlBest ResponseYou've already chosen the best response.0
i got 12j = y , so 12 cows it takes to eat the grass grown in 1 day
 2 years ago
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