Plot hole: Superman (or Kal-El) was a baby when his parents sent him away from Krypton before its destruction, and as Jor-El told his son in his first message he would have already been dead by then for thousands of Superman's years. Kara never existed during any of this yet so somehow she instantly recognizes him from the poster on the wall, even though she should have no idea who he is.
Supergirl (1984)
2 plot holes - chronological order
Directed by: Jeannot Szwarc
Starring: Faye Dunaway, Peter O'Toole, Mia Farrow, Hart Bochner, Helen Slater
Visible crew/equipment: When Selena visits the school, there's a tube reflected on her window. When her car starts to move we see it's part of an umbrella-like structure used for lighting.
Trivia: Helen Slater later played Kara's aunt Lara, the biological mother of her cousin Clark, in Smallville, and Kara's adoptive mother Eliza in the CW's Supergirl.
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Answer: It's never explained, she could have changed at super speed. In Superman II, when confronted by the super criminals at the Fortress of Solitude, Superman did a disappearing and reappearing act. So did the criminals. It might be a similar thing.