Two towns $X$ and $Y$ are connected by a regular bus service. $A$ bus leaves in either direction at every $T$ minutes. $A$ man moving with some speed in the direction $X$ to $Y$ finds that a bus goes past him every $t_1$ minutes in the direction of his motion,and every $t_2$ minutes in the opposite direction. Then $T$ is given by

• A
  $\frac{2 t_1 t_2}{t_1+t_2}$
• B
  $\frac{\left(t_1-t_2\right) t_1}{t_1+t_2}$
• C
  $\frac{2 t_2\left(t_1+t_2\right)}{\left|t_1+t_2\right|}$
• D
  $\frac{t_1 t_2}{\left|t_1-t_2\right|}$