Problema Solution
2 cows in 4 weeks can eat all the grass on 2 acres and all the grass that grows on these 2 acres during the 4 weeks. 3 cows in 2 weeks can eat all the grass on 2 acres and all the grass that grows on these 2 acres during the two weeks. How many cows can eat in 6 weeks all the grass on 6 acres and all the grass that grows on these 6 acres during the 6 weeks? Assume the grass has a constant growth rate and is distributed evenly. HINT: Can be solved by using a 3 by 3 system.
Answer provided by our tutors
Let x = amount of grass one cow can eat in one week,
y= amount of grass which grows on one acre in one week.
Since two cows in four weeks can eat all the grass on two acres and all the grass that grows on these two acres during the four weeks; we have 8x=2y+8z.
Also we know that three cows in two weeks can eat all the grass on two acres plus all the grass that grows on these two acres in two weeks, then 6x=2y+4z.
Now if n represents the minimum number of cows required to eat in six weeks all the grass on six acres and all the grass that grows on these six acres during the six weeks, then 6nx=6y+36z. Eliminating x and y from our three equations (solve for x and y in the first two equations in terms of z, and substitute into the third), we obtain 12nz=60z. Hence n=5.