Round: 304

Suppose you have a grassy field, and Kaus eat grass at a constant rate. Keep in mind, the grass keeps growing continuously.

48 Kaus can clear all the grass off the field in 90 days.

120 Kaus can clear all the grass off the field in 30 days.

How many Kaus would be needed to clear all of the grass in 16 days? Round up to the nearest whole Kau.

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Answer: 215

Let's say that P is the amount of grass in the pasture at the beginning of day 1, and r is the amount of grass that grows in 1 day.

To get the amount of grass 1 kau eats per day, for the 48 kaus over 90 days, we'd get (P + 90r)/(48*90)
To get the amount of grass 1 kau eats per day, for the 120 kaus over 30 days, we'd get (P + 30r)/(120*30)

Since the kaus always eat the same amount, the two formulas are going to be equal.

120 * 30 = 3600, and 48 * 90 = 4320, so:

(P + 90r)/4320 = (P + 30r)/3600.

Solve for P, and we get P=270r, or r = P/270.

Now let's look at the question. We need to find the number of kaus what can clear the field in 16 days. If x is the number of kaus required, 1 kau per day eats:

(P+16r)/(16x)

So, (P+16r)/(16x) = (P + 90r)/4320

And then, substitute P: (270r+16r)/(16x) = (270r + 90r)/4320

286r/16x = 360r/4320

From that, we get x = 214.5.

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