A drug is administered orally. The amount of drug in the GI tract ($X$) and in the bloodstream ($Y$) are modeled by the system of differential equations:\n$\\frac{dX}{dt} = -k_a X, \\quad \\frac{dY}{dt} = k_a X - k_e Y$\nwith $X(0) = D$, $Y(0) = 0$, absorption rate $k_a = 0.5$ hr$^{-1}$, and elimination rate $k_e = 0.1$ hr$^{-1}$. At what time $t_{max}$ is the amount of drug in the bloodstream maximized?