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0 . 7 5 Clue
THE PROBABILITY OF THE ANTS COLLIDING IS 0.75. EACH ANT CAN MOVE IN 2 DIFFERENT DIRECTIONS. BECAUSE THERE ARE 3 ANTS, THIS MEANS THAT THERE ARE 23 (8) POSSIBLE WAYS THAT THE ANTS CAN MOVE. NOW, THERE WILL NEVER BE A COLLISION BETWEEN ANY OF THE ANTS IF THEY ARE ALL WALKING IN THE SAME DIRECTION. AND, THE ONLY TIME THEY WILL BE WALKING IN THE SAME DIRECTION IS IF THEY ARE ALL WALKING EITHER CLOCKWISE OR COUNTER-CLOCKWISE AROUND THE TRIANGLE. SO, THERE ARE ONLY TWO SCENARIOS IN WHICH A COLLISION WILL NOT HAPPEN BETWEEN THE ANTS. THIS MEANS THAT THERE ARE 6 SCENARIOS WHERE THE ANTS WILL COLLIDE. AND 6 OUT OF 8 POSSIBLE SCENARIOS, MEANS THAT THE PROBABILITY OF COLLISION IS 6/8, WHICH EQUALS 3/4 OR 0.75. THUS, THE PROBABILITY OF THE ANTS COLLIDING IS 0.75 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 THIS ONE IS BEST SOLVED WORKING BACKWARDS, THE LAST PART DAVID SPENT HALF OF WHAT WAS LEFT PLUS $1.00 ON CANDY AND THEN WAS OUT OF MONEY. THAT MEANS HE MUST HAVE SPENT $2.00 ON CANDY AS $1.00 WAS HALF OF WHAT HE HAD USING THE SAME LOGIC BACKWARDS: $2.00 ON CANDY $6.00 ON BALLOONS AND STREAMERS $12.00 ON THE CAKE TOTAL OF $20.00 THE TRAIN IS MOVING AT 40 MILES PER HOUR. IMAGINE THAT A FRIEND IS WALKING WITH YOU. WHEN THE TRAIN WHISTLE BLOWS, YOU HEAD AWAY FROM THE TRAIN, HE HEADS TOWARD IT. WHEN HE REACHES SAFETY, YOU WILL BE 6/8 (OR 3/4)OF THE WAY ACROSS THE BRIDGE, AND THE TRAIN WILL HAVE JUST REACHED THE BRIDGE. FOR THE TRAIN TO CROSS 4/4 OF THE BRIDGE IN THE TIME YOU CROSS THE REMAINING 1/4, THE TRAIN MUST BE MOVING FOUR TIMES YOUR SPEED