ANSWER: Before we tackle how long did it take Noah to construct the ark we should cover a little background information about this fascinating man and the incredible feat he accomplished. Noah was born in 2928 B.C. and was 480 years old when God asked him to build a ship to save all the animals and his immediately family. God was bringing a great flood because humans had set their hearts to do evil all of the time (Genesis 6). God gave man one hundred twenty years more to live when he commanded Noah about the ark.
In 2328 B.C., the year of the flood, Noah was six hundred years old (Genesis 9:29). He was a man of faith (Hebrews 11:5 - 7) who walked with God (meaning he obeyed Him and His commandments - see Genesis 6:9 and 1John 2:3 - 6, 5:2 - 3) and who would live a long life of 950 years. It was because he feared the Lord that God chose him to build an ark (ship) to save animals from extinction.
The ark not only was it the biggest ship built up to that time, it would be the largest sailing vessel man would construct until around the 1800's A.D.! It displaced (at a draught of 15 cubits) more than 22,000 tons of water. God told Noah to make a ship that would have over 101,000 square feet (9,383 square meters) of floor space. Because it was built on the 1:6 ratio (50 cubits: 300 cubits) modern naval architecture reveals is the most stable for ocean going vessels, it would be almost impossible to turn the ship over!
Concerning your question about the length of time it took to complete Noah's ship, there is nowhere in Scripture that supports it taking one hundred and twenty years to construct it. This span of time was the period God allowed mankind to live from the time He made His judgment until the flood.
"Now it came to pass, when men began to multiply on the face of the earth, and daughters were born to them, that the sons of God saw the daughters of men, that they were beautiful; and they took wives for themselves of all whom they chose.
"And the Lord said, 'My Spirit shall not strive with man forever, for he is indeed flesh; yet his days shall be one hundred and twenty years.' " (Genesis 6:1 - 3, NKJV throughout)
My research shows there is no evidence regarding the duration it took Noah to build and complete his ark work. Not only was an Internet search silent on the length so was the book of Jubilees and even the historian Josephus. To allow, however, one hundred and twenty years to construct it is extremely excessive, even with the many factors taken into consideration. Obviously, God did not see the need to reveal this rather inconsequential detail. Does it really matter the time it took? What is important is that we learn the spiritual lesson derived from it.
"Now all these things happened to them as examples, and they were written for our admonition, on whom the ends of the ages are come" (1Corinthians 10:11)
Thank you for your question regarding how long it took Noah to build the ark.