For a nuclide decaying by two independent parallel pathways, the total decay rate is the sum of the individual decay constants:

$$\lambda_{total}=\lambda_{\beta}+\lambda_{EC}=\frac{\ln 2}{t_{1/2,\beta}}+\frac{\ln 2}{t_{1/2,EC}}$$

The overall half-life is then $t_{1/2,total}=\dfrac{\ln 2}{\lambda_{total}}$, which simplifies to the familiar “product over sum” (reciprocal-addition) relation:

$$\frac{1}{t_{1/2,total}}=\frac{1}{t_{1/2,\beta}}+\frac{1}{t_{1/2,EC}}$$

$$t_{1/2,total}=\frac{t_{1/2,\beta}\cdot t_{1/2,EC}}{t_{1/2,\beta}+t_{1/2,EC}}=\frac{35.4\times173}{35.4+173}=\frac{6124}{208.4}\approx29.4\text{ d}$$

Notice that combining two decay pathways always makes the overall half-life shorter than either individual half-life, since both processes are removing atoms simultaneously.