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P _ _ N T Clue
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 THE TRAIN IS ABOUT TO LEAVE AND YOU WILL NOT BE ABLE TO CATCH THE TRAIN. THE AMOUNT OF TIME TAKEN TO TRAVEL TO THE HALFWAY POINT AT 15 MILES AN HOUR IS THE SAME AMOUNT OF TIME TAKEN TO REACH THE TRAIN STATION WHEN TRAVELLING TO THE RAILROAD STATION AT 30 MILES AN HOUR. FOR EXAMPLE, LET'S ASSUME THAT THE DISTANCE TO TRAVEL IS 30 MILES. WHEN TRAVELLING AT 30 MILES AN HOUR, IT TAKES 1 HOUR. WHEN TRAVELLING AT 15 MILES AN HOUR, IT WILL ALREADY TAKE 1 HOUR TO REACH THE HALFWAY POINT THERE IS NO WAY TO GET AN AVERAGE SPEED OF 30 MPH (MILES PER HOUR). IF YOUR AVERAGE SPEED FOR THE 2 MILES STRETCH MUST BE 30 MPH, YOU SHOULD DO IT IN 4 MINUTES. DURING THE ASCENT, YOU WOULD HAVE ALREADY TAKEN 4 MINUTES TO TRAVEL 1 MILE AT 15 MPH. SINCE YOU HAVE TAKEN 4 MINUTES TO GO UP THE HILL, YOU WILL NEED TO TAKE 0 SECONDS TO TRAVEL THE 1 MILE DESCENT IN ORDER TO GET AN AVERAGE SPEED OF 30 MPH. THIS IS NOT POSSIBLE THE STATION CLOCK IS 3 MINUTES FAST. THE MORNING JOURNEY TOOK 65 MINUTES, AND THE EVENING JOURNEY THEREFORE TOOK 52 MINUTES, AND THE TRAIN ARRIVED 57 MINUTES AFTER IT SHOULD HAVE LEFT, THAT IS, 3 MINUTES EARLY