Sorry if this is a repeat; I searched and found only one other thread that discussed Expeditious Search...
Preface: I know of no PC with a move higher than 35, most are around 25. This means that maximum speeds are around 250 fpm, with a half speed of 125 fpm. Even a fleet elf with speed 35 has a half speed of 175 fpm.
So how do the 150 and 300 fpm numbers in the definition of Search ever come into play? Even Expeditious Search says "(up to half your Speed)," which seems to nullify its usefulness.
If a PC moves at "full" speed at 250 fpm what are the consequences? Are you no longer taking "educated guesses," (> half speed) or are you still being "thorough and guarantee you checked everything" (< 300 fpm)?
Background Info:
Table 9-2: Travel Speed
Speed Feet per Minute Miles per Hour Miles per Day
10 100 1 8
15 150 1-1/2 12
20 200 2 16
25 250 2-1/2 20
30 300 3 24
35 350 3-1/2 28
40 400 4 32
50 500 5 40
60 600 6 48Search
ConcentrateExploration
Source Core Rulebook pg. 480 2.0
You Seek meticulously for hidden doors, concealed hazards, and so on. You can usually make an educated guess as to which locations are best to check and move at half speed, but if you want to be thorough and guarantee you checked everything, you need to travel at a Speed of no more than 300 feet per minute, or 150 feet per minute to ensure you check everything before you walk into it. You can always move more slowly while Searching to cover the area more thoroughly, and the Expeditious Search feat increases these maximum Speeds. If you come across a secret door, item, or hazard while Searching, the GM will attempt a free secret check to Seek to see if you notice the hidden object or hazard. In locations with many objects to search, you have to stop and spend significantly longer to search thoroughly.Expeditious Search
Feat 7
General
Source Core Rulebook pg. 260 2.0
Prerequisites master in Perception
You have a system that lets you search at great speed, finding details and secrets twice as quickly as others can. When Searching, you take half as long as usual to Search a given area. This means that while exploring, you double the Speed you can move while ensuring you’ve Searched an area before walking into it (up to half your Speed). If you’re legendary in Perception, you instead Search areas four times as quickly.
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A Nimble Elf with Fleet would have 35, and classes like Monk and Swashbuckler grant further increases to that at level 3, so it's pretty easy to have 40+ move speed. By level 19, said Monk would have a move speed of 65, and if you add Boots of Speed that goes up to 70.
Regardless, as for the actual question: A minute is 10 rounds. In Exploration mode, it's assumed that you only take one action per round. In the case of the Search exploration activity, you would Stride one round and Seek the next, and so on. The speed limit is there so that you can't stack on Speed bonuses, like the Monk there, and still claim that you searched everything before walking into the area.
You would still have to only move a max 15 feet per round to ensure you check everything before walking into the area you're checking. This means anyone moving at half speed with a speed higher than 30 would need to slow down to 30. If you move faster than that you can easily walk into a trap without realizing it. Expeditious Search increases this to 30 per round, so a max speed of 60. Our Monk would STILL have to go slightly slower than their normal half speed of 45 to make sure they weren't missing anything.
If you don't care about possibly triggering hazards, then you can move faster, which is the 300 feet per minute part. You still have to move at half speed though.
A Nimble Elf with Fleet would have 35, and classes like Monk and Swashbuckler grant further increases to that at level 3, so it's pretty easy to have 40+ move speed. By level 19, said Monk would have a move speed of 65, and if you add Boots of Speed that goes up to 70.
[rest of excellent explanation deleted]
Wow! I'm a GM that hasn't gone thoroughly enough through all of the PC feats. I hadn't considered that they could boost your speed to such heights.
That does make the description of Search and Expeditious Search make more sense. I wish they had written it better.