A man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 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? Pick one: A) 5 minutes B) 6 minutes C) 8 minutes D) 9 minutes E) 15/2 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 15 minutes a bus overtakes cyclist: \frac{d}{b-c}=15, d=15b-15c;   Every 5 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;   d=15b-15c=5b+5c, --&gt; b=2c, --&gt; d=15b-15b/2=15b/2.   Interval=\frac{d}{b}=\frac{15/2b}{b}=15/2   Answer: 15/2 minutes (15/2 minutes).
<result>E</result>
A man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 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?