The common cold virus whether in adults or children lasts around the same amount of time.
If you have just a common cold virus the cold should last from 7 to 10 days before going away on it's own.
You can take some over the counter cold medicine, stay hydrated and add moisture to the room by using a vaporizer, humidifier or taking a steamy shower and getting plenty of Vitamin C.
When you do that the cold virus should be gone within 10 days and if not then you could have a more serious viral infection such as Pneumonia or something else that may require antibiotics.
If the cold isn't gone within 10 to 14 days you should see your doctor to make sure it's nothing more serious as Pneumonia can be fatal in some cases.
If you're having trouble breathing or have chest pain with the cold then you should always see a doctor because that's normal and is usually a sign of Pneumonia.