Emily has a field with uniformly cut grass of height 2 cm

[luoeugene11]

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[Deleted member 4993]

Emily has a field with uniformly cut grass of height 2 cm which grows at a constant rate. In this field she keeps three animals, a rabbit, a goat and a guinea pig. There is enough grass to feed all three for 20 days, the goat and the rabbit for 25 days, the goat and the pig for 33 days and a third days, and the rabbit and the pig for 50 days. How long would it sustain each animal alone?

Let

the total amount of grass = T

Amount of grass eaten by the goat per day = G

Amount of grass eaten by the pig per day = P

Amount of grass eaten by the rabbit per day = R

Then

20G + 20P + 20R = A → ...................... G + P + R = 0. 05 * A .....................(1)

25 (G + R) = A →................................. G + R = 0.04 * A ....................(2)

100/3(G + P) = A → ............................ G + P = 0.03 * A ....................(3)

50 (P + R) = A → ................................ P + R = 0.02 * A ....................(4)


However, adding (2), (3) & 4 we get →..G + P + R = 0.045 * A → \(\displaystyle \ne\) (1)

So the conditions given are not consistent and thus cannot be solved.