http://www.firefightermath.org/index.php?option=com_content&...
"A 100-foot length of 1-inch diameter hose is charged with water. How many gallons of water are in that length of hose?"
Ugh.
"A 100-foot length of 1-inch diameter hose is charged with water. How many gallons of water are in that length of hose?"
Ugh.
5" supply hose holds about a gallon per foot of water when charged, and water weighs just a little more than 8 lbs per gallon, so a charged 100' section of 5" supply hose weighs over 800 lbs. So make sure you have the hose where you want it before charging it, because it's damn hard to move afterwards and the like.
In terms of doing math on the fireground, at least in a structural fire scenario (wildland firefighting has some other concerns) the single biggest one is usually flow-rate. That is, a crew has stretched a 200' pre-connected 2" attack line, and wants to go in flowing 200 gpm to attack the fire. As the engineer, what pressure do you configure on that discharge to give them their 200 gpm? Here's the kicker though... almost nobody sits there thinking "Well, the friction loss per foot of 2" hose at 200 gpm is x, multiply x by 200, assume a desired pressure of 100 psi at the nozzle, blah, blah, blah.". No, instead somebody precomputed the common configurations, wrote them on an index card, laminated it, and taped it to the pump panel. Plus the engineer probably has the really common ones memorized anyway, and/or has figured out a heuristic that's "good enough".
"How many pints are in a 5-gallon pail? How many cups are in a 5-gallon pail?"
A department can't decide to use metric alone. The entire industry first would need to support at the minimum both standards.
In recent years, the total number of fire deaths is 3000 to 4000 per year:
https://www.usfa.fema.gov/data/statistics/fire_death_rates.h...
Many of those deaths will have happened regardless of the response.
In some sense, across 300 million people, even 3000 is close enough to zero (there's more than 2.5 million total deaths each year in the US). That doesn't mean that improving fire response isn't important, but it might not be a very good place to look for incremental improvements in mortality.
A much bigger issue is the lack of recruitment and volunteerism in the American fire service. People simultaneously don't want to increase property taxes to fund career departments and they also don't want to volunteer. Communities can't have it both ways. Lack of staffing is a far greater risk than whether I'm dividing by 10 or 12.
That problem is still no fun to do in your head. If it's important to do frequently, it's not hard to memorize the constant for "1 ft of 1 in-diameter hose = X gallons" and then multiply as appropriate.
https://motherboard.vice.com/en_us/article/qkvzb5/the-time-n...
The original problem requires plenty of conversions (to cubic inches) and memorization of infrequently used constants (how many cubic inches in a gallon?).
If imperial isn’t your thing, doing it in metric is easier, at least it was for me.