The travel time from Arusha to Tarangire National Park is about 2 to 2.5 hours (depending on traffic and road conditions).
If you do a round trip (Arusha → Tarangire → Arusha) in the same day, the total driving time will be around 4 to 5 hours.
Most people prefer to visit Tarangire, enjoy a full game drive, then continue to stay overnight in Karatu or nearby, instead of going back to Arusha the same day. This saves time and energy for the next day’s safari