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sritama

  • 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.

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  1. experimentX
    • 2 years ago
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    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. sritama
    • 2 years ago
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    yeah...

  3. gingerkid101
    • 2 years ago
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    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

  4. perl
    • 2 years ago
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    what is initial?

  5. gingerkid101
    • 2 years ago
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    the amount of grass that the field had initially

  6. experimentX
    • 2 years ago
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    yeah i figured out that.

  7. perl
    • 2 years ago
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    so you set them equal to each other because you assumed they ate all the grass

  8. gingerkid101
    • 2 years ago
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    I didn't assume, they said that they "cleared the field"

  9. perl
    • 2 years ago
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    errr, that was given

  10. perl
    • 2 years ago
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    so what exactly are you equating , what is your left side and right side

  11. perl
    • 2 years ago
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    total grass grown = total grass eaten (over the days )

  12. gingerkid101
    • 2 years ago
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    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.

  13. perl
    • 2 years ago
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    ok but thats 2 equations in 3 unknowns

  14. perl
    • 2 years ago
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    the grass is growing while they are eating

  15. experimentX
    • 2 years ago
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    grass growth must be some function of days

  16. sritama
    • 2 years ago
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    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

  17. perl
    • 2 years ago
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    well you can subtract equation 1 from equation 2, that eliminates x the initial

  18. sritama
    • 2 years ago
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    by eliminating the initial i will find the relation between m and n

  19. perl
    • 2 years ago
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    how did you get grass growth rate is 90 and 30 ?

  20. perl
    • 2 years ago
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    nevermind

  21. perl
    • 2 years ago
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    that was days

  22. gingerkid101
    • 2 years ago
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    Yeah sritama I was actually just about to correct my equations to add the days on both sides.

  23. sritama
    • 2 years ago
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    yeah,i took the grass growth rate n/each day ... so it must b 90n and 30n

  24. sritama
    • 2 years ago
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    oh ok gingerkid 101

  25. perl
    • 2 years ago
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    ginger can you redo your equation

  26. perl
    • 2 years ago
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    i like your equation, its very logical :)

  27. gingerkid101
    • 2 years ago
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    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

  28. perl
    • 2 years ago
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    yeah thats a little odd, grass per cow per day

  29. perl
    • 2 years ago
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    how does that come out in units, grass/ (cow/day) or

  30. sritama
    • 2 years ago
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    probably it means the amount of grass taken by each cow per day

  31. gingerkid101
    • 2 years ago
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    grass/(cow * day) or grass/cow/day it's all the same.

  32. gingerkid101
    • 2 years ago
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    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.

  33. gingerkid101
    • 2 years ago
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    anyway the equations fully played out are... x + 30y = 3600j x + 90y = 4320j that's what I'm at right now.

  34. perl
    • 2 years ago
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    ok now its linear algebra, one moment

  35. perl
    • 2 years ago
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    x + 30y - 3600j=0 x + 90y- 4320j=0

  36. perl
    • 2 years ago
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    I get x = 3240 j y = 12j j = j

  37. perl
    • 2 years ago
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    actually we know we want 16 , so we have another equation

  38. perl
    • 2 years ago
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    x + 30y = 3600j x + 90y = 4320j x + 16 y = 16 i * j

  39. gingerkid101
    • 2 years ago
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    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

  40. perl
    • 2 years ago
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    how did you get 8 additional cows?

  41. sritama
    • 2 years ago
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    yeah,thats my question too

  42. gingerkid101
    • 2 years ago
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    8 additional to 1/3 of 120. maybe I'm just talking out of my retricenow haha

  43. gingerkid101
    • 2 years ago
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    I don't even know. meh, I never had to do anything like this and I took up to calc 3 haha

  44. perl
    • 2 years ago
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    well this is a solid start

  45. perl
    • 2 years ago
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    i got 12j = y , so 12 cows it takes to eat the grass grown in 1 day

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