- Noah and family enter the ark ---> Noah's age is 600 years + 1 month + 17 days (Genesis 7:11)
- It rained for 40 days and nights (Genesis 7:12,17)
- Waters abated after 150 days (Genesis 8:3)
- Ark rested atop the mountains of Ararat ---> Noah's age is 600 years + 6 months + 17 days (Genesis 8:4)
- Tops of Mountains visible ---> Noah's age is 600 years + 9 months (Genesis 8:5)
- Noah saw dry ground outside the ark ---> Noah's age is exactly 601 years (Genesis 8:13)
- The Earth was dry; Noah and family leave the ark ---> Noah's age is 601 years + 1 month + 27 days (Genesis 8:15-18)
So the total time Noah spent on the ark was 1 year and 10 days (with possibly some small room for adjustment based on differences between Hebrew calendars and modern Gregorian calendars).
That is a long time to spend in a boat with family and animals!