A STUDENT PLT ENTERS THE RWY WITHOUT CLRNC AT BFI WHILE HIS INSTRUCTOR IS DISTR STUDYING A MAP.

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MYSELF AND A STUDENT WERE INVOLVED IN A RWY INFRACTION AT BOEING/KING COUNTY FIELD IN SEATTLE; WA. AFTER LISTENING TO THE ATIS; I CONTACTED BOEING CLRNC DELIVERY AND WAS TOLD TO EXPECT A DEP FROM RWY 31R WITH A W DEP TO VASHON ISLAND AND THEN A TURN SWBOUND REMAINING CLR OF THE SEATTLE CLASS B AIRSPACE. I THEN CONTACTED BOEING GND AND REQUESTED A TAXI CLRNC. WE WERE CLRED TO TAXI TO RWY 31L AND HOLD SHORT BEHIND ANOTHER SMALL CESSNA. I INSTRUCTED MY STUDENT TO FOLLOW THE CESSNA FOR THE TAXI. AS MY STUDENT TAXIED; I STUDIED THE SEATTLE SECTIONAL CHART TO GET A CLR IDEA OF OUR DEP. I WOULD PERIODICALLY LOOK UP TO MAKE SURE MY STUDENT WAS STAYING CLR OF ALL TFC; TAXIING AT A REASONABLE SPD; AND HOLDING TXWY CTRLINE. I CONTINUED THIS DURING OUR TAXI. ABOUT 300 FT FROM A8 (WHERE WE WERE INSTRUCTED TO HOLD SHORT); I NOTICED THE CESSNA WE WERE FOLLOWING CONTINUE HIS TAXI ACROSS RWY 31R TO RWY 31L. MY STUDENT DID NOT REALIZE THAT THE CESSNA HAD CONTACTED BOEING TWR ON THE ROLL AND PROCEEDED TO FOLLOW THE CESSNA ACROSS RWY 31R. AS I GLANCED OUT AGAIN; I REALIZED WHAT WAS GOING ON AND USING MY BEST JUDGEMENT; CONTINUED THE ROLL ACROSS RWY 31R TO CLR THE RWY. I HELD SHORT OF RWY 31L AND BEFORE I COULD CONTACT GND THEY CONTACTED ME AND TOLD ME TO TAXI BACK ACROSS RWY 31R AND CONTACT THEM BY PHONE. THIS SITUATION HAPPENED BECAUSE OF SEVERAL REASONS. #1 WAS THE FACT THAT I WAS NOT SPECIFIC WITH THE STUDENT WITH MY INSTRUCTIONS. I SHOULD HAVE TOLD HIM TO FOLLOW THE CESSNA TO RWY 31R AND HOLD SHORT; JUST AS THE TWR HAD INSTRUCTED. #2 WAS THE FACT THAT I TRUSTED THE STUDENT'S JUDGEMENT; BUT THE FACT IS THAT I AM PIC AS AN INSTRUCTOR AND HAVE THE FINAL SAY ON EVERYTHING. #3 GOES WITH #2 IN THAT I BECAME COMPLACENT BECAUSE I HAD SEEN THE STUDENT DEMONSTRATE EXCELLENT ARPT OPS AND JUDGEMENT IN PAST FLTS AND ASSUMED HE WOULD KNOW WHAT TO DO. #4 IS THAT I RUSHED MYSELF TO A SCHEDULE. IF I HAD ACCEPTED BEING A FEW MINS LATE; I WOULD HAVE BEEN ABLE TO DELAY OUR TAXI AND STUDY THE SECTIONAL WHILE WE WERE STILL HOLDING SHORT AT THE RAMP. INSTEAD; MY HEAD WAS INSIDE THE COCKPIT IN ONE OF THE MOST CRUCIAL PHASES OF FLT; AND AS PIC THAT IS NOT ACCEPTABLE. IN THE END; MY ACTIONS ALL PUT TOGETHER CAUSED A POTENTIALLY EXTREMELY DANGEROUS SITUATION. MY LESSON IS TO ALWAYS SAY THE ANTIDOTE TO 'GET THEREITIS' AND BRING SAFETY FIRST.