Beetle harvest

Classical Mechanics Level 3

A scout from an ant colony (colony A) finds a dead beetle of mass \(M\) a distance \(d_A\) from his colony. At the same time, a scout from another colony (colony B) who is distance \(d_B\) from his colony, also finds the beetle. If ants from colony B can walk at speed \(v_B\), and workers from \(A\) can each carry the mass \(\delta m\) of ant flesh at any given time, what is the slowest speed (in m/s) at which workers from colony A walk so that workers from colony B never catch up and steal the beetle pieces?

Details

If an ant from colony B catches an ant from colony A, it will kill the ant from colony A.
If an ant from colony A makes it to colony A with beetle flesh, he is safe from workers from colony B.
The scouts both start out at the beetle.
\(d_A=3\) m
\(d_B=5\) m
\(v_B=5\) m/s
\(M=250\) g
\(\delta m=0.5\) g

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