Engine Cooling problem
1989 Pontiac Sunbird 4 cyl Automatic

My radiator is pushing water back into the reserve after the car has been running for some time. Each time I turn off the car, after driving it for about half an hour at a steady speed of 60mph, I can hear the water boiling in the reserve. The reserve is now amlost full with greenish colored water. I have tested the fan and it is working. It kicks in when the the thermostad indicator climbs to half and cools down the radiator within a minute. What do you think is wrong? How can I fix it?

Thank you kindly,

Adonis.