Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?

• A
  $\frac{a + f}{2(1 + b)}$
• B
  $\frac{f - a}{2(1 + b)}$
• C
  $\frac{a + f}{1 + b}$
• D
  $\frac{a + f}{2(b - 1)}$