Three runners on 2.5km circular track start at same point, speeds 8, 10, 12 km/h. From 9am to 3pm, how many times meet at start?

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Accepted Answer

1. Lap times: for speeds 8, 10, 12 km/h on a 2.5 km track we get $5/16$ h, $1/4$ h, $5/24$ h.

2. Write with common denominator 48: $15/48,\;12/48,\;10/48$. The LCM of numerators is $60$, so the common return time is $60/48=5/4$ h = $1.25$ h.

3. From 9am to 3pm is $6$ hours. They meet at the start every $1.25$ hours, at times $0,1.25,2.5,3.75,5.0$ hours after 9am.

4. Total meetings (including 9am) = 5 times.

FINAL_ANSWER: c

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Answer

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