In a park there are three concentric circular running tracks. Radius of \( 2^{\text {nd }} \) tr....

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In a park there are three concentric circular running tracks. Radius of \( 2^{\text {nd }} \) track is double of first and of \( 3^{\text {rd }} \)
\( \mathrm{P} \)
track is triple of first. Three runners are running on these tracks with constant speed. When the runner in the first track completes one round, the runner in 2nd has completed half round and the runner in third track has completed quarter round. If the accelerations of the runners are in ratio \( \alpha: \beta: \gamma \), where \( \alpha, \beta \& \gamma \) are least integers, then find the value of \( \frac{\alpha+\beta+\gamma}{3} \).


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