Hot water enters a well$-$insulated mixer at $80C$ at a mass flow rate of $0\mathrm{.}5$ kg$/$s and cold water enters the mixer at $20C$ and if the water exits the mixer at $)=(4\mathrm{.}18k\frac{J}{k}gK$ Determine the following:

a$.$ Draw the system, labeling the inlet and outlet temperatures and flow rates.

b$.$ State any assumptions and governing equations

c$.$ Find the flow rate for the cold wate $($kg$/$s$)$