They died of dehydration.
Not radiation poisoning...that's why the accelerated demise.
Human beings can last barely two days with nothing to drink...a fact which most people who have a go at this film don't seem to realise.
They didn't get chance to die of radiation poisoning...they surely would have died from it...but the lead up to their death and Jim's rare outburst of 'What are we going to drink for *beep* sake?'...shows what led to their deaths at the end...the man was thirsty.