Problem $05\mathrm{.}154-$ Heat exchanger

In large steam power plants, the feedwater is frequently heated in a closed feedwater heater by using steam extracted from the turbine at some stage. Steam enters the feedwater heater at $1$ MPa and $195\mathrm{.}0C$ and leaves as saturated liquid at the same pressure. Feedwater enters the heater at $2\mathrm{.}5$ MPa and $50C$ and leaves at $10C$ below the exit temperature of the steam. Determine the ratio of the mass flow rates of the extracted steam and the feedwater. The enthalpies of steam and feedwater are $h_1=2815\mathrm{.}576k\frac{J}{k}g,h_2=762\mathrm{.}51k\frac{J}{k}g,T_2=179\mathrm{.}9C,h_3=209\mathrm{.}34k\frac{J}{k}g,$ and $h_4=718\mathrm{.}55k\frac{J}{k}g.($Round the final answer to three decimal places.$)$

The ratio of the mass flow rates is