A hot$-$water stream at $80\backslash$deg C enters a mixing chamber with a mass flow rate of $0\mathrm{.}500$ kg$/$s where it is mixed with a stream of cold water at $20\backslash$deg C$.$ If it is desired that the mixture leave the chamber at $42\backslash$deg C$,$ determine the mass flow rate of the cold$-$water stream. Assume all the streams are at a pressure of $250$ kPa. The enthalpies are $335\mathrm{.}02$ kJ$/$kg$,83\mathrm{.}915$ kJ$/$kg$,$ and $175\mathrm{.}90$ kJ$/$kg$.$ The saturation temperature at a pressure of $250$ kPa is $127\mathrm{.}41\backslash$deg C$.($Round the final answer to three decimal places.$)$ An illustration of mixing chamber features two sloping inlets on the left and a horizontal outlet on the right.This illustrates depicts a mixing chamber consisting of three pipelines: two sloping pipelines and one horizontal pipeline. The first sloping pipeline is labeled T subscript $1$ equals $80$ degrees Celsius and m over dot subscript $1,$ while the second sloping pipeline is labeled t subscript $2$ equals $20$ degrees Celsius and m over dot subscript $2.$ The horizontal pipeline is labeled H $2$ O $($P equals $250$ kilopascals$)$ and T subscript $3$ equals $42$ degrees Celsius. Arrows entering the mixing chamber through the sloping pipelines on the left and exiting through the horizontal pipeline on the right indicate the direction of the flow of substances.The mass flow rate is kg$/$s$.$