Beetle harvest

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