A Hike Unlike Any Other

RAY: A guy named Bruce Douglas sent this puzzler in just a couple of weeks ago. I had to reobfuscate, but not a whole lot. He writes,

"My wife and I like to go hiking and several years ago, like another of your listeners, Dinesh, we spent lots of time in Death Valley trying to kill ourselves. Then two years ago we hiked in the Florida Everglades and my wife's brother came along on that trip. He wasn't too good at staying on the trails or heeding the various warning signs about alligators and such and that would explain why we now call him 'Lefty.'

'But last year, we went hiking someplace where the trails are marked in time and not distance. For example if we wanted to go from two points that were 12 miles from Point A to Point B then the sign would read perhaps 4.5 hours instead of 12 miles.

"On this particular day, we were planning to hike from Point A to Point C via Point B, where we would stop for lunch. At the outset the trail markers told us that it was 8 hours from A to C.

"At Point B where we stopped for lunch, we had our lunch and got ready to get back on the trail. The markers told us that it was 3 hours back to Point A and 3 hours to Point C. These signs proved to be completely accurate. How could this be?'

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