Where do people come up with the idea that it took Noah 120 years to build the Ark? If you read Genesis chapters 5 through 8 it plainly states that he was 500 when God told him to build it and Gen 8:11 states that in the six hundredth year of Noah’s life, in the second month, on the seventeenth day of the month, they entered the ark and vs 16, the Lord shut him in. That’s 100 years, not 120.
The reference to 120 years comes from Genesis 6:3 and is the length of time from God’s first warning of a coming judgment to the Great flood. Earlier, in Genesis 5:32, we’re told that after Noah was 500 years old he became the father of Shem, Ham and Japeth. When God made the covenant with Noah his sons were old enough to have wives (Genesis 6:18) and Genesis 7:6 tells us Noah was 600 years old when the flood came. Genesis 11:10 says Shem had his 100th birthday 2 years after the flood.
The Bible doesn’t say how long it took Noah and his sons to build the ark. But by piecing the available information together we can guess it was no more than 60 years and some speculate they could have done it in much less time.