How do you come up with 31? We see her as little more than a toddler in flashbacks just before the power goes out and the power has only been out 15 years.
This show is somewhat entertaining but your suspension of disbelief has to be off the scale. 15 years without power and every light and appliance magically turns back on at the flick of a switch? They aren't even trying.
Tighr is talking about the actress, not the character. According to wikipedia there's no actual age listed for her. Some sources have her DOB listed as 1988 which would mean she was 12 years old when she graduated High School so unless she was Doogie Howser I doubt that.
Let's say she was 17 in 2000 when she graduated HS. That puts her at 30 now which means she's only 13 years younger than the woman playing her Mother in the show.