A man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? Choose the correct option
A) 5 minutes  B) 6 minutes  C) 8 minutes  D) 9 / 2 minutes  E) 10 minutes

Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 9 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 9 , d = 9 b - 9 c ; every 3 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 3 , d = 3 b + 3 c ; d = 9 b - 9 c = 3 b + 3 c , - - > b = 2 c , - - > d = 9 b - 9 b / 2 = 9 b / 2 . interval = \ frac { d } { b } = \ frac { 9 / 2 b } { b } = 9 / 2 answer : d ( 9 / 2 minutes ) ."
Answer: D