[Suicide Junkie]

The two final positions are variables, and unknown. But they are equal to each other by definition, since equal positions is the definition of interception.
Knowing that they are both equal reduces the number of unknowns by one (Instead of positionA and positionB, you have two copies of positionIntercept). This allows you to solve for Time. If the interception is impossible, Time will end up being an imaginary number.