A single, $30$ cm diameter, well draws from a nearly horizontal, unconfined sandy$-$gravely aquifer with a depth of $20$ m below the ground surface. Two observation wells are located at radius $\backslash (\backslash$mathrm$\{$r$\}\_\{1\}=10\backslash$mathrm$\{$~m$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$r$\}\_\{2\}=100\backslash$mathrm$\{$~m$\}\backslash )$ from the pumping well. The aquifer materials have a porosity of $0\mathrm{.}35$ and saturated hydraulic conductivity of $\backslash (20\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$d$\}\backslash ).$ Without the well the water table is approximately horizontal and $2$ m below the ground. Below the aquifer material is impermeable bedrock.

a$)$ What is the maximum discharge $($in $\backslash (\backslash$mathrm$\{$m$\}^\{3\}/\backslash )$ day$)$ that can be drawn from the well if the maximum allowable drawdown in the well, relative to the static level, is $\backslash (2\backslash$mathrm$\{$~m$\}?\backslash )(10$ marks$)$

b$)$ How long would it take for a conservative tracer to travel the distance between the observation wells? $(10$ marks$)$