The Passenger train and the goods train

            Two trains, a passenger train and a goods train, is running in the same direction on parallel railway tracks. The passenger train takes three times as long to pass the goods train –even when they are going in the opposite directions.

            If the trains run at uniform speeds, how many times faster than the goods train is the passenger train moving?

Answer:      When the trains are moving in opposite directions, they are passing each other with combined speeds of the trains. Hence when going in the same direction, the ‘passing speed’ is the speed to the passenger speed minus the speed of the goods train.

                  If the passenger train goes twice as fast as the goods train, then the passing speed when going in the opposite direction will be 2 plus 1 or 3 compared with 2 minus 1 or 1 when the trains are going in the same direction.

                  Therefore the answer is twice as fast.