Beetle harvest

A scout from an ant colony (colony A) finds a dead beetle of mass MM a distance dAd_A from his colony. At the same time, a scout from another colony (colony B) who is distance dBd_B from his colony, also finds the beetle. If ants from colony B can walk at speed vBv_B, and workers from AA can each carry the mass δm\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.
  • dA=3d_A=3 m
  • dB=5d_B=5 m
  • vB=5v_B=5 m/s
  • M=250M=250 g
  • δm=0.5\delta m=0.5 g
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