The problem is solved by ejecting the girl, Marilyn, into space and to her death.
The problem is that Marilyn stowed away on a space transport, headed for a planet where her brother is a colonist. She has not seen him in ten years. The planet's human colonists experience an epidemic, and the ship is launched to take them medicines; without them, the colonists will die. The ship has *exactly* enough fuel to complete its mission, and no more. Marilyn does not realize this. She thinks she will get in some trouble, have to pay a fine, but it will be worth it to see her brother. The ship's captain tries to figure out some way to save both Marilyn and the colonists, but there is no way around the numbers--the ship does not have enough fuel to transport her, and she is sacrificed to save the colony.