the water in your radiator is rusty because your antifreeze/water ratio is not correct. Antifreeze serves two important functions: protecting the cooling system at temperature extremes and inhibiting rust and corrosion in the system. When your antifreeze/water ratio is not correct Rust and sediment can accumulate in the cooling system. This can eventually clog your cooling system mainly your radiator and cause your car to overheat, and more serious problems with the over heating. I would suggest flushing your system and adding the correct antifreeze/water ratio mixture. Doing this your self or having it done by proffessional.
When a car is hot, keep the car running and add water to the radiator. When a car is cold, you can simply put the water into the radiator.
When engine is cool, Look in radiator and see if the antifreeze is full. Mechanics use more information of problem to diagnose, like, Where is leak at under the car? Air conditioners can cause water drip from car but that is normal. No matter what is causing the drip you will also need to clean/fix the problem that is causing the rusty color too.
Check where this rusty water is coming from. There are many possible causes.
lack of proper care. lack of proper (distilled) water in the radiator.
Water
A radiator cools the water that flows around the engine.
remove your radiator form your car then poor some hot water in radiator till water comes out nice and smooth.
There are several causes that will reduce the water level in your car radiator. The most common cause is evaporation. Engine overheating will also reduce the radiator water level.
Pure distilled water.
See saturnfans.com Barnowl posted a home made procedure for radiator flushing.
The radiator cools the water which then goes to your engine to cool it off, as cool water enters your engine hot water from the engine enters your radiator
In a car the water pump circulates coolant through the engine and to the radiator.