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?
Choose the correct choice from the following
A) 5 minutes
B) 6 minutes
C) 8 minutes
D) 9 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 18 minutes a bus overtakes cyclist: \frac{d}{b-c}=18, d=18b-18c;   Every 6 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=6, d=6b+6c;   d=18b-18c=6b+6c, --&gt; b=2c, --&gt; d=18b-9b=9b.   Interval18 -9= 
<gadget id="calculator">18 -9</gadget>
<output>9</output>
9b.   Interval=\frac{d}{b}=\frac{9b}{b}=9   Answer: 9 minutes (9 minutes).
<result>D</result>
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?