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On PHB P 182 it mentions that "While traveling at a fast pace, characters take a - 5 penalty to their passive Wisdom (Perception) scores to notice hidden threats.". It also has a chart for travel pace:

Travel Pace

Pace      Distance Traveled per...      Effect
          Minute   Hour      Day        

Fast      400 ft   4 miles   30 miles   -5 penalty to passive Wisdom (Perception) 

Normal    300 ft   3 miles   24 miles   —

Slow      200 ft   2 miles   18 miles   Able to use stealth

However it also says "Certain special mounts, such as a pegasus or griffon, or special vehicles, such as a carpet of flying, allow you to travel more swiftly."

Does the "Fast" pace on the chart apply to all travel (air, land, sea), and if not, what is the Fast Pace for flying travel. If it matters, assume a base fly speed of 50ft.

If possible, looking for RAW answers and please note references or attach citations. Thx.

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There is no RAW answer for this in the books, so you have to calculate it.

However you have already supplied the necessary information to calculate these in the speed chart provided under Travel Pace. Of note: 1 mile = 5280 feet.

From the chart we assume one day of travel is 8 hours of actual travel:

Fast = 665 ft per minute / 7.5 miles per hour / 60 miles per day

Normal = 500 ft per minute / 6 miles per hour / 45 miles per day

Slow = 335 ft per minute / 4 miles per hour / 30 miles per day

The values here have been rounded to the nearest half. The fast and slow pace are set based on Travel Pace at 1/3 plus or minus normal speed.

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    \$\begingroup\$ I think it'd be worth explaining that you're scaling everything up by 5/3, on the assumption that the printed table's "indexed" to a base speed of 30'/round. \$\endgroup\$ – nitsua60 Aug 14 '16 at 15:49
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    \$\begingroup\$ I think the normal speed of 300 ft / minute already covers that assumption in the table itself. \$\endgroup\$ – Lino Frank Ciaralli Aug 14 '16 at 17:45
  • \$\begingroup\$ This chart was originally used for ground travel. While flying is faster (50ft/round rather than 30ft/round), it's also easier. Though I suppose being conservative is better. \$\endgroup\$ – Al Sun Aug 15 '16 at 17:45
  • \$\begingroup\$ While this is covering what the distance traveled would be, I think it's ignoring the penalty aspect. Personally, I think the original speeds are good for deciding when to assign the penalty, as it's based on a normal character's perception. For example, if they had a mount that moved at the speed of light it would not be reasonable (IMO) to let the character to make Perception checks without penalty when they pass something at half the speed of light, because it's "slow" for that mount. \$\endgroup\$ – sirjonsnow Apr 30 '18 at 14:58

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