Cows feeding

[capnx]

This is a question from an exercise book. the explanation was really confusing (and long), so I thought maybe someone could offer some shortcut version.

A farm has a piece of land that has grass growing at an even speed. The land can sustain 27 cows for 6 weeks and 23 cows for 9 weeks. How many weeks can the land sustain 21 cows?

7 weeks
8 weeks
12 weeks
18 weeks
24 weeks

[spoiler]The solution says it's similar to a works problem but with changing workload, and breaks the steps down to finding initial grass and new growing grass and has a total of 3 steps.. Wondering if there's a shorter way.
OA is 12 weeks. [/spoiler]

[fruti_yum]

This is a question from an exercise book. the explanation was really confusing (and long), so I thought maybe someone could offer some shortcut version.

A farm has a piece of land that has grass growing at an even speed. The land can sustain 27 cows for 6 weeks and 23 cows for 9 weeks. How many weeks can the land sustain 21 cows?

7 weeks
8 weeks
12 weeks
18 weeks
24 weeks

[spoiler]The solution says it's similar to a works problem but with changing workload, and breaks the steps down to finding initial grass and new growing grass and has a total of 3 steps.. Wondering if there's a shorter way.
OA is 12 weeks. [/spoiler]

I worked it out as a slope change!! got 10.5 weeks which is not even in the answer choices!! what did i do wrong?

[regor60]

Let G=growth rate/week; R=cow consumption rate(1/cow-week)

key point: cows consume initial land plus growth over the period: 1+ time* growth rate

1+6G= 27*R*6 > 27 cows
1+9G= 23*R*9 >23 cows
solve for G, R > 15/72 and 1/72 per week,respectively

find time T for 21 cows

1+15/72 * T = 21*1/72*T

T=72/6 > 12

[aakar]

I need to understand how to do this via an equation, I just did it by guessing really.

if it takes 27 cows to get through 6 weeks, and 23 cows to get through 9 weeks, the difference between the weeks and the # of cows seems relatively small..

If you drop 4 cows it gives you an extra 3 weeks. Thus for 21, I just assumed that the number should be around 3-4 weeks. A & B seem too small and D&E seem too large...

Thus 12..

[regor60]

Educated guessing is good, but only if you can't determine a better approach. Take a look a my earlier response, those are the equations

[adr]

Is there a simpler method than the one mentioned above which is solved by equations - didnt get that!