A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 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 the correct option
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 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;   Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;   d=12b-12c=4b+4c, --&gt; b=2c, --&gt; d=12b-6b=6b.   Interval12 -6= 
<gadget id="calculator">12 -6</gadget>
<output>6</output>
6b.   Interval=\frac{d}{b}=\frac{6b}{b}=6   Answer: 6 minutes (6 minutes).
<result>B</result>
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 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?