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T H _
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T R _ _ N Clue
THE STUDENT IS DOUBLE COUNTING A LOT OF THE DAYS. A LOT OF THE TIME SPENT SLEEPING, EATING, AND RELAXING OCCURS DURING WEEKENDS AND THE SUMMER. WEEKENDS ALSO OCCUR DURING THE SUMMER, SO ALL OF THESE HOURS ARE GETTING COUNTED SEVERAL TIMES. AND, SCHOOL IS NOT AN ALL DAY AFFAIR. SO THE 4 DAYS ACTUALLY REPRESENTS MORE DAYS OF SCHOOL. IF SCHOOL IS 6 HOURS PER DAY, THOSE FOUR DAYS REPRESENTS 16 DAYS OF SCHOOL IF THE GIRLS HAD BEEN ON A STANDING TRAIN, THE FIRST GIRL'S CALCULATIONS WOULD HAVE BEEN CORRECT, BUT THEIR TRAIN WAS MOVING. IT TOOK 5 MINUTES TO MEET A SECOND TRAIN, BUT THEN IT TOOK THE SECOND TRAIN 5 MORE MINUTES TO REACH WHERE THE GIRLS MET THE FIRST TRAIN. SO THE TIME BETWEEN TRAINS IS 10 MINUTES, NOT 5, AND ONLY 6 TRAINS PER HOUR ARRIVE IN THE CITY ONE TRAIN WAS RUNNING TWICE AS FAST AS THE OTHER. LET: SPEED OF THE FAST TRAIN = F SPEED OF THE SLOW TRAIN = S TIME IT TAKES FOR THE TRAINS TO MEET (PASS EACH OTHER) = T SINCE BOTH TRAINS TRAVEL THE SAME TOTAL DISTANCE AND DISTANCE = TIME X SPEED: F(T+1) = S(T+4) WE'RE TRYING TO FIGURE OUT F/S WHICH IS EQUAL TO (T+4) / (T+1) FROM THE EQUATION ABOVE. SO WE NEED TO FIGURE OUT THE VALUE OF T. AFTER THEY MEET, THE FAST TRAIN TRAVELS ONE MORE HOUR AT SPEED F AND COVERS THE SAME DISTANCE THE SLOW TRAIN COVERED IN T HOURS: F1 = ST OR F = ST AFTER THEY MEET, THE SLOW TRAIN TRAVELS FOR 4 MORE HOURS AND COVERS THE SAME DISTANCE THE FAST TRAIN COVERED IN T HOURS: S4 = FT SUBSTITUTING ST FROM THE FIRST EQUATION IN FOR F IN THE 2ND EQUATION: 4S = STT 4 = TT 2 = T SUBSTITUTE 2 IN FOR T IN THE (T+4) / (T+1) EQUATION TO GET 6/3 OR 2. THE FAST TRAIN IS GOING TWICE AS FAST AS THE SLOW TRAIN THE TIME IS 6AM. FOR EVERY 1 HOUR THAT HAS PASSED, THE CLOCK WILL ONLY SHOW 36 MINUTES AS IT WILL LOSE 24 MINUTES. WHEN THE CLOCK WAS SHOWING 3AM, 180 CLOCK MINUTES HAVE PASSED SINCE MIDNIGHT. THIS MEANS THAT 300 (180/36 X 24 MINUTES + 180 MINUTES) REAL MINUTES HAVE PASSED WHEN THE CLOCK WAS SHOWING 3AM. SINCE THE CLOCK STOPPED 1 HOUR AGO, ANOTHER 60 MINUTES HAVE PASSED. THEREFORE A TOTAL OF 360 MINUTES HAVE PASSED. SINCE 360 MINUTES = 6 HOURS, THE TIME IS 6 HOURS AFTER MIDNIGHT