4 9
M _ N _ T _ S .
I T
_ S
V _ R Y
T _ M P T _ N G
T _
J _ S T
S _ B T R _ C T
T H _
T _ M _ S
9 : 0 9
F R _ M
1 0 : 1 0 ,
_ T C . ,
_ N D
G _ T
6 1
M _ N _ T _ S ,
_ R
_ F
Y _ _ ' R _
C _ R _ L _ S S
G _ T
1 0 1
M _ N _ T _ S .
H _ W _ V _ R ,
T H _ N K
_ F
T H _
T _ M _ S
C L _ S _ S T
T _
_ N _
_ N _ T H _ R ,
1 2 : 1 2
_ N D
1 : 0 1 ,
_ N D
Y _ _
W _ L L
F _ N D
T H _
D _ F F _ R _ N C _
_ S
4 9
M _ N _ T _ S 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 49 MINUTES. IT IS VERY TEMPTING TO JUST SUBTRACT THE TIMES 9:09 FROM 10:10, ETC., AND GET 61 MINUTES, OR IF YOU'RE CARELESS GET 101 MINUTES. HOWEVER, THINK OF THE TIMES CLOSEST TO ONE ANOTHER, 12:12 AND 1:01, AND YOU WILL FIND THE DIFFERENCE IS 49 MINUTES YES. HE TOOK AS MUCH TIME FOR THE SECOND HALF OF HIS TRIP AS THE WHOLE TRIP WOULD HAVE TAKEN ON FOOT. SO NO MATTER HOW FAST THE TRAIN WAS, HE LOST EXACTLY AS MUCH TIME AS HE SPENT ON THE TRAIN. HE WOULD HAVE SAVED 1⁄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