A student studies the kinetics of two gaseous decomposition reactions carried out in separate rigid containers at constant temperature:

Reaction 1: \(\text{A(g)} \xrightarrow{\text{catalyst}} 2\,\text{C(g)}\), which follows zero-order kinetics with rate constant \(k_1\).

Reaction 2: \(\text{B(g)} \rightarrow \text{D(g)} + \text{E(g)}\), which follows first-order kinetics with rate constant \(k_2\).

In an initial experiment with \([\text{A}]_0 = 0.10 \text{ M}\) and \([\text{B}]_0 = 0.10 \text{ M}\), the half-life of Reaction 1 and the half-life of Reaction 2 are both measured to be \(60 \text{ s}\). If the experiment is repeated at the same temperature with \([\text{A}]_0 = 0.20 \text{ M}\) and \([\text{B}]_0 = 0.20 \text{ M}\), what is the value of the ratio \(\dfrac{t_{1/2}\text{ of Reaction 1}}{t_{1/2}\text{ of Reaction 2}}\) in the second experiment?