Amar, Akbar and Anthony start running in the same direction...

Amar, Akbar and Anthony start running in the same direction and from the same point, around a circular track with speeds $7 \mathrm{~m} / \mathrm{sec}, 11 \mathrm{~m} / \mathrm{sec}$ and $22 \mathrm{~m} / \mathrm{sec}$ respectively. If Akbar can complete 5 revolutions around the track in $40 \mathrm{sec}$, when will they meet for the first time after they start? (A) $56 \mathrm{~s}$ (B) $88 \mathrm{~s}$ (C) $118 \mathrm{~s}$ (D) $79 \mathrm{~s}$

Amar, Akbar and Anthony start running in the same direction and from the same point, around a circular track with speeds $7 \mathrm{~m} / \mathrm{sec}, 11 \mathrm{~m} / \mathrm{sec}$ and $22 \mathrm{~m} / \mathrm{sec}$
respectively. If Akbar can complete 5 revolutions around the track in $40 \mathrm{sec}$, when will they meet for the first time after they start?
(A) $56 \mathrm{~s}$
(B) $88 \mathrm{~s}$
(C) $118 \mathrm{~s}$
(D) $79 \mathrm{~s}$

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Key Concepts

Least Common Multiple (LCM) in Synchronization

When multiple objects move periodically but with different periods, they will only align at the starting point after an interval equal to the least common multiple of their individual lap times. Using the LCM is crucial for determining the first common meeting time, where all individual cycles coincide.

Periodic Motion on Circular Tracks

In circular motion, an object repeatedly follows a closed path, returning to its starting point after each complete lap. This concept explains how each runner, moving at a constant speed, will have a fixed lap time, and it sets the stage for analyzing when the runners will coincide on the track.

Speed-Distance-Time Relationship

This concept involves the formula distance = speed × time, which is essential for calculating how far a runner travels in a given time period. In problems involving motion, it allows us to determine variables like the track's circumference or the time taken for one revolution when speeds and distances are provided.

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