Two identical conducting rods are first, connected independently to two vessels, one containing water at 100^oC and the other containing ice at 0^oC. In the second case, rods are joined end to end and are connected to the same vessels. If ${\mathrm{q}}_1\text{ and }{\mathrm{q}}_2$ (in g/s) are the rates of melting of ice in two cases, then the ratio of ${\mathrm{q}}_1/{\mathrm{q}}_2$ is ______.