AN OVER-LONG APCH BRIEFING CAUSED AN ACR CREW TO START DOWN LATE RESULTING IN AN ALT DEV XING RESTR NOT MET.

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I WAS GIVING IOE TO A NEW CAPT UPGRADE. THERE WAS ALSO A 'CHK ENGINEER' GIVING IOE TRAINING TO A NEW ENGINEER. AS WE WERE PROCEEDING DIRECT TO ZID VOR; ATC GAVE US A CLRNC TO CROSS 30 MI OUT OF RID AT 13000 FT. WE WERE AT FL240 ABOUT 65 MI SW. AT THE TIME WE RECEIVED THE CLRNC; WE WERE VERY BUSY TRYING TO BRIEF THE APCH AT DAY. AFTER FINISHING THE BRIEFING; WE STARTED DOWN BUT REALIZED IT WOULD BE CLOSE. WE CROSSED THE 30 MI FIX BTWN 13500 FT AND 13800 FT AND LEVELED AT 13000 FT BY 28 MI. CONTRIBUTING FACTORS: FATIGUE; WE HAD ALL BEEN UP AT LEAST 18 HRS AND I HAD BEEN UP WITH NO SLEEP FOR 20 HRS. WORKLOAD; WITH 2 STUDENTS ON BOARD; PERFORMING THE VARIOUS FUNCTIONS TAKES LONGER. THE BRIEF FOR THE APCH AND PREPARATION TAKES LONGER. BECAUSE WE WERE TRYING TO ACCOMPLISH A VARIETY OF PRE-LNDG DUTIES; I DID NOT MENTALLY CALCULATE A DSCNT POINT AS SOON AS I RECEIVED THE CLRNC. HAD I DONE THIS; I WOULD HAVE REALIZED I NEEDED TO START DOWN RIGHT AWAY. WX; WE WERE IN ICING CONDITIONS AND MODERATE TURB MOST OF THE FLT. THESE FACTORS ADD TO MENTAL STRESS. IN THE FUTURE; WHENEVER I RECEIVE A CLRNC FROM ATC; IT MUST TAKE PRECEDENCE OVER BRIEFINGS. IN OTHER WORDS; 'FLY THE AIRPLANE FIRST.'