Answer:

According to the Genesis account, it rained for 40 days., the waters continued to rise until the 150th day, and the floods receded sufficiently for Noah and his family to emerge from the ark after ten months and two weeks.  Probably there is some wiggle room in the last period, as the exact length of time between Genesis 8:5 and Gen 8:15 is not exactly clear.   It is possible that these numbers are approximations.  Besides, it is not clear that the point of the story is to establish the exact number of days, but I would say that the length of time was approximately 10×30 + 14 = 314 days.  Or to be more careful, one might say that it was a little less than one year.

John Oakes