Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sritama

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

  • This Question is Closed
  1. experimentX
    Best Response
    You've already chosen the best response.
    Medals 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
  2. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah...

    • 2 years ago
  3. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  4. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    what is initial?

    • 2 years ago
  5. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 0

    the amount of grass that the field had initially

    • 2 years ago
  6. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i figured out that.

    • 2 years ago
  7. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    so you set them equal to each other because you assumed they ate all the grass

    • 2 years ago
  8. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 0

    I didn't assume, they said that they "cleared the field"

    • 2 years ago
  9. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    errr, that was given

    • 2 years ago
  10. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    so what exactly are you equating , what is your left side and right side

    • 2 years ago
  11. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    total grass grown = total grass eaten (over the days )

    • 2 years ago
  12. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  13. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but thats 2 equations in 3 unknowns

    • 2 years ago
  14. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    the grass is growing while they are eating

    • 2 years ago
  15. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    grass growth must be some function of days

    • 2 years ago
  16. sritama
    Best Response
    You've already chosen the best response.
    Medals 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
  17. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    well you can subtract equation 1 from equation 2, that eliminates x the initial

    • 2 years ago
  18. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    by eliminating the initial i will find the relation between m and n

    • 2 years ago
  19. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get grass growth rate is 90 and 30 ?

    • 2 years ago
  20. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    nevermind

    • 2 years ago
  21. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    that was days

    • 2 years ago
  22. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah sritama I was actually just about to correct my equations to add the days on both sides.

    • 2 years ago
  23. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah,i took the grass growth rate n/each day ... so it must b 90n and 30n

    • 2 years ago
  24. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok gingerkid 101

    • 2 years ago
  25. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    ginger can you redo your equation

    • 2 years ago
  26. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    i like your equation, its very logical :)

    • 2 years ago
  27. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  28. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah thats a little odd, grass per cow per day

    • 2 years ago
  29. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    how does that come out in units, grass/ (cow/day) or

    • 2 years ago
  30. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    probably it means the amount of grass taken by each cow per day

    • 2 years ago
  31. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 0

    grass/(cow * day) or grass/cow/day it's all the same.

    • 2 years ago
  32. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  33. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  34. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    ok now its linear algebra, one moment

    • 2 years ago
  35. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    x + 30y - 3600j=0 x + 90y- 4320j=0

    • 2 years ago
  36. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    I get x = 3240 j y = 12j j = j

    • 2 years ago
  37. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    actually we know we want 16 , so we have another equation

    • 2 years ago
  38. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    x + 30y = 3600j x + 90y = 4320j x + 16 y = 16 i * j

    • 2 years ago
  39. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  40. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get 8 additional cows?

    • 2 years ago
  41. sritama
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah,thats my question too

    • 2 years ago
  42. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 0

    8 additional to 1/3 of 120. maybe I'm just talking out of my retricenow haha

    • 2 years ago
  43. gingerkid101
    Best Response
    You've already chosen the best response.
    Medals 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
  44. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    well this is a solid start

    • 2 years ago
  45. perl
    Best Response
    You've already chosen the best response.
    Medals 0

    i got 12j = y , so 12 cows it takes to eat the grass grown in 1 day

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.