Sounds like you have a leaky heater core. You will need to replace the heater core and give the cooling system a good flushing, it shouldn't be rusty.
Check where this rusty water is coming from. There are many possible causes.
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Is the temperature and pressure valve leaking in your water heater?
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This is an indication that your heater core is leaking. To stop the leaking you will have to replace the heater core or stop using your heater.
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Could be a heater hose
roof or heater core leaking roof or heater core leaking
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