The Apostle Peter gives us the key to this question when he wrote, "One day with the Lord is as a thousand years," (2 Peter 3:8). Father Adam began to die as soon as he was barred from the garden of Eden. 

In the garden, he could eat from all the trees bearing edible fruit and also from the tree of life. "And out of the ground the LORD God made every tree grow that is pleasant to the sight and good for food. The tree of life was also in the midst of the garden," Genesis 2:9. He was sustained by their life-giving fruits. But after his disobedience, he was thrust out into the unprepared earth, and an angel with a flaming sword kept Adam from eating from the tree of life. "So He drove out the man; and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life," Genesis 3:24. 

Adam would die just as God declared, "but of the tree of the knowledge of good and evil, you shall not eat, for in the day that you eat of it you shall surely die," Genesis 2:17. The dying began when he could no longer eat from the tree of life, and continued gradually for nine hundred and thirty years until he died. This all took place within a thousand year day.