Whilst Alexander Galkin gives some great information, I think there's a fundamental reason why that particular pain relief strategy is best, and it hasn't been mentioned yet.
The reason is simply that when you take Ibuprofen or Paracetamol (a full dose) you can only take it once every 4 hours. However, the pain relief doesn't last for 4 hours, so if you take either or both together every four hours you will experience pain after the medication wears off and before you are allowed your next dose.
So instead you can follow either of two strategies:
- Take a full dose of Paracetamol at 0 hours, 4 hours, 8 hours, as well as taking a full dose of Ibuprofen at 2 hours, 6 hours, 10 hours. This will give you less time when no pain medication is in effect. But if your pain is inflammation related you might want to keep the anti-inflammatory effects of Ibuprofen topped up, so you can...
- Take a half dose of Paracetamol + a half dose of Ibruprofen every 2hours. This gives you a mix of pure pain relief and anti-inflammation and ensures minimum time when each medication has no effect.
I don't think human biology has to come into it (apart from the fact that you can take the two substances together with no ill effects), it's just a good pain-avoidance strategy.