In the steam cracking of methane, the following two independent reactions occur at \(1000 \mathrm{~K}\) and 1 bar:

\[ \begin{align*} \mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}+3 \mathrm{H}_{2} \tag{A}\\ \mathrm{CO}+\mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \tag{B} \end{align*} \]

At \(1000 \mathrm{~K}\) and \(1 \mathrm{bar}\), the equilibrium constants for the reactions (A) and (B) are \(K_{\mathrm{A}}=30\) and \(K_{\mathrm{B}}=1.5\). Determine the composition of the product gases leaving the reactor. Assume that the reaction mixture behaves like an ideal gas.