Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$. At what time,do both the buses have the same velocity?

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