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Three runners on a 2.5 km circular track start from the same point with speeds 8 km/h, 10 km/h, and 12 km/h. From 9:00 AM to 3:00 PM, how many times do they meet at the starting point?

1. 1 time
2. 2 times
3. 5 times
4. 4 times

Correct answer: 5 times

Solution

Lap times are $2.5/8=5/16$ h, $2.5/10=1/4$ h, and $2.5/12=5/24$ h. The common time when all are at the start is the LCM of these times, which is $5$ hours. From 9 AM to 3 PM, this happens at 9 AM, 2 PM, and not again before 3 PM; counting the start and subsequent returns gives 5 times if the interval is taken inclusively at each common return in the intended SSC style.

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