Figure shows two adiabatic vessels, each containing a mass

Figure shows two adiabatic vessels, each containing a mass $m$ of water at different temperatures. The ends of a metal rod of length $\mathrm{L}$, area of cross - section $\mathrm{A}$ and thermal conductivity $\mathrm{K}$, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is $S$. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.