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Cows are always hungry...

  • 70 Cows eat all the plants on a pasture in 24 days.
  • 30 Cows clear the same pasture in 60 days.

How many cows are needed to clear the pasture by the end of 96th day?

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closed as off-topic by Lopsy, xnor, Len, Tryth, McMagister Jan 14 '15 at 1:19

  • This question does not appear to be about creation and solving of puzzles, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This is a textbook math problem. I don't think it's actually a puzzle. $\endgroup$ – xnor Jan 13 '15 at 20:22
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    $\begingroup$ IMO, this question belongs on math.SE. $\endgroup$ – Lopsy Jan 13 '15 at 20:48
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20 cows.

The 70 cows over the 24 days eat 1680 cow-nom units.
The 30 cows over the 60 days eat 1800 cow-nom units.

Based on the growth from 24 days to 60 days, we can work out that at 96 days, the cows would need to eat 1920 cow-nom units. Divide that by the 96 days and we get $20 cows$.

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    $\begingroup$ Can we assume that the growth is linear? $\endgroup$ – Ivo Beckers Jan 14 '15 at 9:39
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Since 70 cows clear the pasture in 24 days, we know that there should be more than $70*23=1610$ and at most $70*24=1680$ cow-days of plants in the pasture.

Since 30 cows clear the pasture in 60 days, we know that there should be more than $30*59=1770$ and at most $30*60=1800$ cow-days of plants in the pasture.

Here we run into a problem - the two ranges don't overlap. Either there's an error in the question, or we have to deal with plants growing (they do that).

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  • $\begingroup$ yes, its normal for plants to grow $\endgroup$ – Rafe Jan 13 '15 at 20:38
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First Try

>>> (70 * 24 + 30 * 60) / (2 * 96)
18.125

It looks like you need 18 cows for 96 days.

Second Try

>>> (30 * 60) / (70 * 24) / (60 - 24) * (96 - 60) * (30 * 60) / 96
20.08928571428571

After looking at what others had to say, it might be 20 cows instead.

In more detail, it the previous calculation can be read as follows:

>>> food_for_24_days = 24 * 70
>>> food_for_60_days = 60 * 30
>>> ratio_of_increase = food_for_60_days / food_for_24_days
>>> ratio_of_increase_per_day = ratio_of_increase / (60 - 24)
>>> increase_from_60_to_96_days = ratio_of_increase_per_day * (96 - 60)
>>> food_for_96_days = food_for_60_days * increase_from_60_to_96_days
>>> cows_needed_for_96_days = food_for_96_days / 96
>>> cows_needed_for_96_days
20.08928571428571
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  • $\begingroup$ By your answer it looks like you need 19. Unless you have 1/8 of a cow handy. $\endgroup$ – Paul Jan 13 '15 at 19:58
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    $\begingroup$ @Paul Assume a spherical cow with half the diameter… $\endgroup$ – Gilles Jan 13 '15 at 21:46

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