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Another more probable thing to do might be visiting Mud Island in the Mississippi River. It is separated from downtown Memphis by a small lagoon. A suspended monorail runs between downtown and Mud Island, so it does become a rail-related activity. It travels at the breakneck speed of 7 mph and the long journey is 1/3 of a mile. Have fun trying to do the math and figure out from that how much time the trip takes! The monorail is suspended from a pedestrian bridge, so it's possible to walk as well. But what fun would that be for this group of railfans?
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Mud Island Monorail is also known as Memphis Suspension Railway. This Wikipedia page includes a short video clip of the train approaching the downtown station.
Once on Mud Island, the first link above shows what activities there are to do. It may be our best way to kill time, and if it's a very hot day, an island in the river is probably a good place to be. One of the elements of Mud Island is the Riverwalk, a scale replica of the Mississippi River shoreline from Illinois down to the Gulf of Mexico (including New Orleans where we will have just been) right alongside the real river.