Two rods of the same length and the same cross-section are made of materials with thermal conductivities $K$ and $2K$. Heat flows through them from a hot body at a fixed temperature into a vessel of ice at $0^\circ\text{C}$. When the rods are joined end to end, a certain amount of ice melts in $18$ minutes. If the same two rods are placed side by side between the same two bodies, the same amount of ice melts in