Three individuals depart simultaneously traveling in identical directions around a circular path having an 11-kilometer perimeter. Their individual paces are 4, 5, and 8 kilometers per hour respectively. At what point will they rendezvous back at the starting location?
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Answer: A. 11 hours
Explanation
Lap times around the eleven kilometer path are determined by dividing the track length by each speed. Finding the least common multiple of the individual lap time fractions yields the rendezvous time. All three individuals meet back at the starting location precisely after eleven hours of continuous travel. Rendezvous points on circular paths occur when individuals complete an integer number of laps. The time to meet at the start is the LCM of the individual times taken to complete one full circuit. Lap time equals the circular track perimeter distance divided by the individual movement speed.
Athletic training coordinators calculate runner synchronization intervals on circular running tracks. Orbital mechanics evaluate satellite rendezvous times and recurring alignment positions around planetary bodies. Industrial engineers study conveyor belt synchronization where different components cycle at varying speeds. Option b represents a miscalculated LCM that fails to synchronize all three runners simultaneously. Option c vastly overestimates the time required due to incorrect fractional time compounding. Option d assumes a multiple of the correct meeting time rather than the first rendezvous point.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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