Skyhawk 172/Cutlass 172
Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Communication Breakdown; Workload; Situational Awareness; Time Pressure; Confusion
Conflict NMAC
Student Pilot was under the hood as we began to fly back in to ZZZ on the Arrival. We where located about 2 miles south of lake at 1;500 ft. receiving the ATIS when PIC noticed over taking traffic that was only around 500 ft. above us. The traffic continued to fly directly behind us and began to descend down from 2;000 ft. The traffic was essentially over the top of us at around 200 ft. when PIC took controls and executed an emergency descent to avoid collision. The closest the two airplanes got was 100 ft. according to the onboard G1000 traffic. PIC then attempted to contact the traffic on the practice area frequency to no avail. PIC then contacted Dispatch to ask that the PIC of Aircraft Y to speak with me at the conclusion of both events to discuss the incident. When I confronted the PIC of Aircraft Y he said that he did see me and was talking to  Approach at the time and did not see any issues with the incident. The PIC stated that it was not hazardous or reckless and did not understand why I had an issue with the incident.
C172 Flight Instructor described a NMAC while on arrival.