A tank contains $50kg$ of a liquid at $25C.$ At $t=0,$ valves are opened such that the same liquid at $80C$ flows in at $10k\frac{g}{m}in$ through one pipe and it also flows in $(5k\frac{g}{m}in)$ at $50C$ in another pipe. A liquid stream $(15k\frac{g}{m}in)$ exits the bottom of the tank at temperature $T.$ The tank is very well mixed $($but with negligible shaft work$),$ very well insulated, and its contents always have a uniform temperature. What is the temperature of the effluent liquid stream after these flows have been running for $5$min $?$ How long does it take for the effluent stream to get within $1C$ of its steady state temperature? $($ANS: $60C,12\mathrm{.}7$min $)$