Police said that as a result of the arrests officers were now conducting a scene examination at a Bishopdale address.
They are appealing for any sightings of a grey 1994 Nissan Cefiro travelling between Ruskin St, Addington, and Leeston on the evening of Sunday 24 April or the morning of Monday 25 April.
"These arrests have been the result of a hard-working and highly skilled team of investigators," said Detective Inspector Tom Fitzgerald.
"This has been a challenging inquiry, but my staff have worked tirelessly throughout the week to ensure the family of Mr Tucker have some answers."
"I'd also like to thank the community for their support and understanding so far. We've received an excellent response from them in terms of information throughout our investigation."
Mr Fitzgerald could not comment on the specifics of the investigation as the matter was now before the courts.
