Mikrislac wrote: ↑Mon Aug 10, 2020 11:20 pm
Two runners are racing on a circular track that is 500 m long. They start from the same point on the track and run in the same direction. The ratio of their speeds is 2 : 3. The faster runner travelled a total distance of 8 km. How many times did the runners meet each other on the track? (1 km = 1000 m)
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
The runners meet whenever the faster runner completes ONE MORE LAP than the slower runner.
The ratio of their speeds = 2 : 3.
Implication:
Every time the faster runner completes 3 laps, the slower runner completes only 2 laps, with the result that the faster runner completes one more lap than the slower runner and meets the slower runner.
Thus:
The total number of meetings = the total number of 3-lap trips completed by the faster runner.
Distance traveled by the faster runner = 8 km = 8000 meters
Since each lap = 500 meters, we get:
Number of laps completed by the faster runner = 8000/500 = 16 laps.
Since the faster runner travels a total of 16 laps, the number of 3-lap trips completed by the faster runner = 5.
The correct answer is
E.
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