MATH CHALLENGE!!!!! ?

Question

This Math Challenge is called the COW CHALLENGE!

Say that 70 cows take 24 days to eat all the grass in a pasture. The same pasture sustains 30 cows for 60 days. How many cows would take 90 days to eat all the grass?

Answer 1

Let's suppose the pasture measures 100 m2.

So, 70 cows would eat 100 m2/24 days. Their daily speed would be 4.166 m2/d (the 70 of them), and 1 cow would eat 0.059 m2/d

Then, 30 cows would eat 100 m2/60 days. Their daily speed would be 1.666 m2/d, and 1 cow's would be 0.055 m2/d

Finally, x cows would eat 100m2/90 days. Their daily speed would be 1.111 m2/d, and 1 cow's would be 1.111/x



Let's grab the second situation and set a proportion. 0.055 m2/d:1 cow::1.111 m2/d:x. Do the math: 1.111/0.055= 20.2. Since I rounded the numbers (well, not "rounded", just not using all of their decimals), obviously the result would have never be exact, so I may round the result as well. And the answer I got is 20 cows...

Answer 2

Here's what I got...



We have x amount of grass in which 70 cows take 24 days to eat, thus:



it will take 70 cows per 24 days to eat all 100% of x

70 cows / 24 days = 1*x



The pasture sustains 30 cows for 60 days, so:



it will take 30 cows for 60 days to eat some percentage, p, of x

30 cows / 60 days = p*x



We know x = 70 cows / 24 days, so:

30 cows / 60 days = p*(70 cows / 24 days)

p = 12 / 70



So, it takes 30 cows 60 days to eat 12 / 70 of x (the total amount of grass)



30 days are left and 1 - 12 / 70 = 58 / 70 of the grass must still be eaten



So, c cows / 30 days = (58 / 70)*x

again x = 70 cows / 24 days



c cows / 30 days = (58 / 70) * (70 cows / 24 days)

c cows = 145 cows / 2



c = 145 / 2 or 73 more cows

A total of 73 + 30 = 103 cows

Answer 3

It would take 45 cows to eat all the grass in 90 days because if you take 30 cows for 60 days minus it with the 90 days

= 90d - 60 = 30 days left

so you'd take the 30 cows and divide it by 2



30 / 2 = 15

30 cows + 15 more cows = 45 cows with 60d +30d = 90d

Answer 4

ratios.



60 x (3/2) = 90, thus 30 / (3/2) = # of cows for 90 days. 20 cows.

Answer 5

straight line equation

x-70/30-70=90-24/60-24

x=-3.32

actually 1 cow will eat it in 86 days only