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sritama
 3 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.
sritama
 3 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.

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experimentX
 3 years ago
Best ResponseYou've already chosen the best response.048 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. ??

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0no 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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0the amount of grass that the field had initially

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0yeah i figured out that.

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0I didn't assume, they said that they "cleared the field"

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

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0the 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
 3 years ago
Best ResponseYou've already chosen the best response.0ok but thats 2 equations in 3 unknowns

perl
 3 years ago
Best ResponseYou've already chosen the best response.0the grass is growing while they are eating

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

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

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

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah sritama I was actually just about to correct my equations to add the days on both sides.

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

perl
 3 years ago
Best ResponseYou've already chosen the best response.0ginger can you redo your equation

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0x + 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
 3 years ago
Best ResponseYou've already chosen the best response.0yeah thats a little odd, grass per cow per day

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

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0grass/(cow * day) or grass/cow/day it's all the same.

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0in 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.

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0anyway the equations fully played out are... x + 30y = 3600j x + 90y = 4320j that's what I'm at right now.

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

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

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

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

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

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0However, 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
 3 years ago
Best ResponseYou've already chosen the best response.0how did you get 8 additional cows?

sritama
 3 years ago
Best ResponseYou've already chosen the best response.0yeah,thats my question too

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.08 additional to 1/3 of 120. maybe I'm just talking out of my retricenow haha

gingerkid101
 3 years ago
Best ResponseYou've already chosen the best response.0I don't even know. meh, I never had to do anything like this and I took up to calc 3 haha

perl
 3 years ago
Best ResponseYou've already chosen the best response.0well this is a solid start

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