Two rods - one made of steel, the other of zinc - need to be sized such that at $0^{\circ}$ C, $a=1 \mathrm{~m}$, and at $100^{\circ}$ C, their combined length is $b=1.0024 \mathrm{~m}$. What is the length of each rod at $0^{\circ}$ C, given that the linear expansion coefficient of steel is $\lambda^{\prime}=0.000011$, and that of zinc is $\lambda^{\prime \prime}=0.000031$?