C-172 EXHIBITED PARTIAL LOSS OF POWER. PLTS DECLARED EMER AND PERFORMED SUCCESSFUL EMER LNDG AT NEAREST ARPT.

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WHILE ACTING AS A CFI TRAINING ANOTHER PLT TO BE CHKED OUT AT ZZZ; WE EXPERIENCED A PARTIAL LOSS OF ENG PWR IMMEDIATELY AFTER EXECUTING A CLB FROM A LOW APCH INTO RWY 31 AT ZZZ. THE OTHER PLT; WHO WAS FLYING; IMMEDIATELY LOWERED THE NOSE TO MAINTAIN BEST GLIDE; WHILE USING OUR EXCESS AIRSPD AND MOMENTUM TO GAIN SOME ALT. WE SIMULTANEOUSLY COMPLETED ALL EMER CHKLISTS; AND MADE AN IMMEDIATE R TURN THAT WOULD RESULT IN A SHORT FINAL APCH TO ZZZ1. WHILE THE TURN WAS INITIATED; I CONTACTED ZZZ1 TWR; AND DECLARED AN EMER; ADVISING THAT WE HAD LOST SOME OF OUR ENG PWR AND WERE GOING TO LAND ON RWY 9. THE TWR CTLR TOOK IMMEDIATE ACTION TO INSTRUCT AN ACFT ON SHORT FINAL FOR RWY 27 TO GO AROUND ON THE N SIDE OF THE RWY; SO AS NOT TO BE A FACTOR. THE WINDS FROM THE LAST RPTED METAR WERE 300 DEGS AT 13 KTS GUSTING 19 KTS. AT THAT TIME; I TOOK CTL OF THE ACFT; SPOTTED THE OTHER AIRPLANE GOING AROUND; AND MADE AN UNEVENTFUL LNDG ON THE RWY. TWR ASKED IF WE NEEDED A TOW AND ANY FURTHER ASSISTANCE; TO WHICH I RESPONDED 'NO' SINCE WE STILL HAD SOME ENG PWR TO MAKE IT TO OUR HANGAR. THIS EMER HAD A SUCCESSFUL OUTCOME DUE TO THE CRM BTWN MYSELF AND THE OTHER PLT (ALSO A LICENSED CFI); EFFICIENT COM AND ACTION TAKEN BY THE TWR CTLR; IMMEDIATE DECISION TO TURN TOWARD RWY 9; WHICH WAS WITHIN A REACHABLE DISTANCE; AND THE TAILWIND THAT INCREASED OUR GND SPD TOWARDS THE RWY TO HELP US MAKE IT IN. AS A RESULT; BOTH MYSELF AND THE OTHER PLT EXPERIENCED NO INJURIES AND THE ACFT WAS NOT DAMAGED.