Problem 2.248

Two rods whose lengths are $l_{1}$ and $l_{2}$ and heat conductivity coefficients $x_{1}$ and $x_{2}$ are placed end to end. Find the he at conductivity coefficient of a uniform rod of length $l_{1}+l_{2}$ whose conductivity is the same as that of the system of these two rods. The lateral surfaces of the rods are assumed to be thermally insulated.