$($b$)$ A pumping well penetrates the full depth of a confined, isotropic and homogeneous aquifer of infinite extent. Pumping has been maintained at a rate of $\backslash (1,000\backslash$mathrm$\{$~m$\}^\{3\}/\backslash )$ day for $50$ minutes, and the drawdown at an observation well located at a distance of $100$ m from the pumping well is now at $1$ m $.$ If this pumping rate is maintained constant, how long does it take for the drawdown at a second observation well located at a distance of $400$ m from the pumping well to reach $1$ m $?($Give you answer in minutes from the initiation of pumping.$)$