If two acres of pasture are grazed by three cows in two weeks and the same two a
ID: 3069293 • Letter: I
Question
If two acres of pasture are grazed by three cows in two weeks and the same two acres are also grazed by two cows in four weeks, how many cows will eat all the grass in six acres during six weeks, assuming the grass grows uniformly and at a constant rate? 1. A kangaroo can jump a distance of nine jumps while it takes a hare 13 jumps to cover the same distance. If eight jumps of the hare are equivalent to three kangaroo jumps, how much will the kangaroo jump before it reaches the hare knowing that the hare has a head start of seven of its jumps ahead of the kangaroo? 2.Explanation / Answer
1) Here we need to know 2 variables. How much of Grass is there and how much the grass grows.
a = grass eaten by a cow in 1 week = grass/cow per week
b = amount of grass/acre and
c = the amount of grass that grows per week (this is at a constant rate)
Grass eaten by 3 cows in 2 weeks = 3 cows x 2 weeks x a grass/cow per week = 6a grass
What is this amount equal to which the cows have eaten = amount of grass in the 2 acres + the grass that would have grown in 2 weeks on these 2 acres. = 2xb + 2 x 2 x c = 2b + 4c
Therefore we get 6a = 2b + 4c --------- (1)
Similarly when 2 cows graze on 2 acres for 4 weeks, we get 2 x 4 x a = 2 x b + 4 x 2 x c
Therefore 8a = 2b + 8c ------- (2)
Performing equation 2 - equation 1, we get
8a - 6a = 2b + 8c - (2b + 4c)
2a = 4c, therefore a = 2c.
Putting a = 2c in equation 1, we get 6 x (2c) = 2b + 4c
therefore 8c = 2b or b = 4c
Now, with this we need to find how many cows can graze for 6 week in 6 acres. Let Y, be the number of cows. Then Y x 6 x a = 6 x b + 6 x 6x c
putting a = 2c and b = 4c, we get 12Yc = 24c + 36c = 60c
Therefore Y, the number of cows = 5.