Many commercial sinks and publicly-accessible showers have mixing valves underneath them, which pre-mix the hot and cold water to obtain a comfortable temperature at the faucet. Federal regulations (the ADA) specify a maximum temperature at the shower- head of a public shower of 120 degree F, and current EPA best-practice showerheads deliver 2 gallons/minute of flow. You are installing a mixing valve, and must set the hot and cold water How rates to obtain the desired performance in the worst-case scenario. The hot water heater supplies water at a temperature of 150 degree F (and you are not limited by flow rate - set it for whatever you need). The cold water in the summer comes into the house at 70 degree F, but in the winter it comes in at 50 degree F. In the summer (the high-temperature scenario, worst-case per the regulations), de-termine the flow rates (in gallons/minute) of hot and cold water required to obtain the specified temperature and flow rate at the faucet. Once the valve is installed, however, it is not easy to get at and service. So, in the winter, given the flow rates from part a and the lower temperature cold water feed, what will be the temperature of the water coming out the showerhead?