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?
Choices: A) 5 minutes B) 6 minutes C) 8 minutes D) 9/2 minutes E) 10 minutes
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=9b-9c;   Every 3 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=3, d=3b+3c;   d=9b-9c=3b+3c, --&gt; b=2c, --&gt; d=9b-9b/2=9b/2.   Interval=\frac{d}{b}=\frac{9/2b}{b}=9/2   Answer: 9/2 minutes (9/2 minutes).
<result>D</result>
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?