The Elephant Diet

Answer: $\frac13$ kg


Using words
Elephant portion = 365 rabbit portions
Rabbit portion = 1 rabbit portion
Total = 366 rabbit portions
366 rabbit portions = 122 kg
1 rabbit portion = 122$\div$366 = $\frac13$ kg of carrots.


Using algebra
Suppose the rabbit eats $r$ kg of carrots each day.

Then the elephant eats $365r$ kg of carrots each day.

Together, they eat 122 kg of carrots, so $$\begin{align} r+365r&=122\\ \Rightarrow 366r&=122\\ \Rightarrow r&=\tfrac{122}{366}\\ \Rightarrow r&=\tfrac13\end{align}$$