This seems to be the intent of the problem:
At 12pm, John, Vicky and David all start running from the same point around a 100-meter circular track. John and David run in one direction, while Vicky runs in the opposite direction. John runs at a speed of 2 meters per second, Vicky at a speed of 2.5 meters per second, and David at a speed of 5 meters per second. How many seconds will have passed when the three runners meet for the second time?
A) 100/3 B) 200/3 C) 100 D) 400/3 E) 200
David and John:
When people travel in the same direction, SUBTRACT THEIR RATES.
David's rate - John's rate = 5-2 = 3 meters per second.
Thus, every second, David SURPASSES John by 3 meters.
To meet John, David must surpass John by the ENTIRE LENGTH OF THE TRACK (100 meters).
Time required = (track length)/(rate difference) = 100/3 seconds.
Thus, every 100/3 seconds, David will surpass John by the entire length of the track.
In other words, David and John will MEET every 100/3 seconds.
David and Vicky:
When people travel in opposite directions, ADD THEIR RATES.
The reason is that the people are WORKING TOGETHER to cover the distance between them.
David's rate + Vicky's rate = 5 + 2.5 = 15/2 meters per second.
Thus, every second, David and Vicky cover 15/2 meters between them.
Since the track is 100 meters, David and Vicky will MEET every time they work together to cover 100 meters between them.
In other words, David and Vicky will meet each time they travel a MULTIPLE of 100 meters.
Since David and John meet every 100/3 seconds, we need to determine how many intervals of 100/3 seconds must pass for David and Vicky to travel a multiple of 100 meters.
Distance traveled by David and Vicky in 100/3 seconds = r*t = (100/3)(15/2) = 250 meters.
Since 100/3 seconds = 250 meters, 200/3 seconds = 500 meters, which is a multiple of 100.
Thus, all 3 runners will meet every 200/3 seconds, implying that they will meet for the SECOND TIME after 400/3 seconds.
The correct answer is
D.
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