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IT WILL TAKE 2 HOURS TO MEET. METHOD 1: IGNORE THE SPEED OF THE STREAM, AS THE BOBBER WILL BE CARRIED ALONG AT THREE MILES PER HOUR AS WILL YOU. IT TAKES TWO HOURS TO TRAVEL FOURTEEN MILES, AT A RATE OF SEVEN MILES PER HOUR. METHOD 2: AS THE BOBBER TRAVELS AT 3 MPH, IT WILL BE SIX MILES CLOSER TO YOU IN TWO HOURS. THE DISTANCE BETWEEN YOU AND THE BOBBER BECOMES 8 MILES (14 - 6). IN TWO HOURS YOU WOULD HAVE TRAVELLED 8 ( (7-3) X 2 ) MILES 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 YOU WILL HAVE TO LIE AWAKE FOR 1 HOUR TO BE SURE OF THE TIME. THE STRIKE YOU HEARD WAS EITHER 1:00 AM OR SOME HALF HOUR. IF, AFTER ANOTHER HALF HOUR YOU HEAR TWO OR MORE STRIKES, YOU KNOW WHAT HOUR IT IS, BUT IF YOU AGAIN HEAR ONE STRIKE, YOU MAY HAVE HEARD SUCCESSIVELY 12:30 AM AND 1:00 AM OR 1:00 AM AND 1:30 AM. AFTER ANOTHER HALF HOUR YOU EITHER HEAR 1 STRIKE (1:30 AM) OR TWO STRIKES (2:00 AM)