At approximately 09:05 MDT, a Cessna 172Q and a Cessna T210N collided while on approach four miles west of the Greeley-Weld County Airport. Each plane contained a rated pilot receiving flight instruction. None of the four pilots were injured and both airplanes landed safely at Greeley. VMC prevailed and both airplanes were on IFR flight plans. The instructor in the 172 requested radar vectors for an ILS approach to runway 9 and canceled his IFR flight plan after turning onto the final approach. During that time he said he heard the controller clear the 210 for a VOR-A approach. The 172 instructor changed to the Unicom frequency and reported he was on a four-mile final to runway 9. Shortly afterward, the pilot of the 210 announced that he was on a four-mile final to runway 9. The 210 struck the 172 from behind and below.