Grass in pasture grows equally thick and at a uniform rate. It takes 2

Question

Grass in pasture grows equally thick and at a uniform rate. It takes 24 days for 70 cows to graze the pasture completely. However if there were only 30 cows, they could graze the entire pasture for 60 days. How many cows will graze the entire pasture in 96 days?

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32

Show Answer

Official Answer

C

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32

GreatII · Answer

Short Cut
60/24 ~~ 70/30
2.5 ~~ 2.333
96/24 ~~ 4 ,

New Cows ~~ 70*2.5/2.33/4 ~~~ 20

Long way
24X70 C = Farm + 24 G ( speed of Growth)
30X60 C = Farm + 60 G

Gives 
10 C = 3 G

Farm = 1680C - 80 C
Farm = 1600 C

96C*N = 1600 + 96 G
96C*N = 1600 + 320C
96 CN = 1920
N = 20 
24C*70 = G

rollinbusiness · Answer

24 days * 70 cows means the field requires 1680 "cow days" of work

60 days * 30 cows means the field requires 1800 "cow days" of work

So when there are fewer cows, the field requires more work (I wonder if cows work slower in a less competitive work environment?)

90 days means we have fewer than 30 cows, but the cows must do more than 1800 cow days of work

So I just tested options:

90 days * 18 = 1620 "cow days"
90 days * 20 = 1800 "cow days"
90 days * 25 = 2250 "cow days"

So the only option that will take more than 60 days, but also have more than 1600 "cow days" of work is 25

IMO answer is C

Regor60 · Answer

The cows consume the original field plus any growth rate occurring during the time that they are grazing.

Set g equal the growth rate and r equal the cows eating rate.

1+24G = 70*24*R

1+60G = 30*60*R

Subtracting the top from the bottom:

36G = 120R so G=10R/3

Substituting G back into the first equation:

1+80R = 1680R and R=1/1600. Therefore G = 1/480.

So how many cows are necessary to graze the field fully over 96 days ?

1+96(1/480) = 96*C/1600

(576/480) =96C/1600.

C = (576*1600)/(480*96) = (10*576)/(3*96) =(10*24)/(3*4) = 20 Cows

Grass in pasture grows equally thick and at a uniform rate. It takes 2

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Grass in pasture grows equally thick and at a uniform rate. It takes 2

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