A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 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?	Select:
A) 5 minutes
B) 6 minutes
C) 8 minutes
D) 9 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 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) .
Answer: D