Lily and her twin sister Lana saved 25 dollars each week to buy a video game how long will it take for them to get 675 dollars

Lily and Lana saved a total of $25 x 2 = $<<25*2=50>>50 each week.

For them to reach $675, it will take them $675 / $50 = <<675/50=13.5>>13.5 weeks.
Since they cannot have a fraction of a week, it will take them 14 weeks to reach $675. Answer: \boxed{14}.