A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from $30 ^ { \circ }$ to $45 ^ { \circ }$, then the time taken (in $\min$ ) by the car to reach the foot of the tower is\\
(1) $\frac { 9 } { 2 } ( \sqrt { 3 } + 1 )$\\
(2) $9 ( \sqrt { 3 } + 1 )$\\
(3) $18 ( \sqrt { 3 } - 1 )$\\
(4) $9 ( \sqrt { 3 } - 1 )$