FCTC Firefighter Math Applications Questions and Answers 2 — Questions and Answers
Question 1: A fire hose delivers 150 gallons per minute (GPM). If a structure fire requires a total of 4,500 gallons to suppress, how many minutes will it take?
- 20 minutes
- 30 minutes (Correct answer)
- 45 minutes
- 60 minutes
Correct answer: 30 minutes
4,500 gallons divided by 150 GPM equals 30 minutes.
To find time, divide total volume by flow rate: 4,500 / 150 = 30 minutes. This calculation is essential for estimating water supply duration during firefighting operations and planning when to establish a secondary water supply.
Question 2: A ladder is placed against a building so the base is 8 feet from the wall and the ladder is 17 feet long. How high up the wall does the ladder reach?
- 9 feet
- 15 feet (Correct answer)
- 12 feet
- 13 feet
Correct answer: 15 feet
Using the Pythagorean theorem: the square root of (17 squared minus 8 squared) equals the square root of 225, which equals 15 feet.
The ladder, wall, and ground form a right triangle. 8 squared plus height squared equals 17 squared, so height squared equals 289 minus 64 equals 225, and height equals 15 feet. Proper ladder placement math ensures safe and effective ladder operations on the fireground.
Question 3: A fire station responds to an average of 12 calls per day. How many calls would the station respond to in a 30-day month?
- 300
- 340
- 360 (Correct answer)
- 420
Correct answer: 360
12 calls per day multiplied by 30 days equals 360 calls.
Simple multiplication: 12 times 30 equals 360 calls per month. Tracking monthly call volume helps fire departments plan staffing levels, equipment maintenance schedules, and resource allocation for peak demand periods.
Question 4: A 2.5-inch hose line has a friction loss of 15 psi per 100 feet. What is the total friction loss for 300 feet of hose?
- 30 psi
- 45 psi (Correct answer)
- 50 psi
- 60 psi
Correct answer: 45 psi
15 psi multiplied by 3 (the number of 100-foot sections in 300 feet) equals 45 psi.
Friction loss is proportional to hose length. 300 feet equals three 100-foot sections, so 15 psi times 3 equals 45 psi total friction loss. Engine operators use this calculation to set correct pump discharge pressure so nozzles receive adequate operating pressure.
Question 5: If a building's floor area is 60 feet by 80 feet, what is the total floor area in square feet?
- 4,200 sq ft
- 4,800 sq ft (Correct answer)
- 5,400 sq ft
- 6,400 sq ft
Correct answer: 4,800 sq ft
60 multiplied by 80 equals 4,800 square feet.
Multiplying length by width gives area: 60 times 80 equals 4,800 sq ft. Knowing floor area helps firefighters estimate required water flow rates using formulas such as the National Fire Academy formula (GPM equals area divided by 3 for a fully involved structure).
Question 6: A firefighter uses a 1.75-inch hose line flowing at 125 GPM. If the tank holds 500 gallons and no water supply is established, how many minutes can the crew operate?
- 2 minutes
- 4 minutes (Correct answer)
- 6 minutes
- 8 minutes
Correct answer: 4 minutes
500 gallons divided by 125 GPM equals 4 minutes of operating time.
500 divided by 125 equals 4 minutes. This highlights the critical need to establish a water supply quickly, as a 500-gallon booster tank is depleted in only 4 minutes at a typical attack line flow rate.
FCTC Firefighter Math Applications Questions and Answers 2
A fire hose delivers 150 gallons per minute (GPM).
If a structure fire requires a total of 4,500 gallons to suppress, how many minutes will it take?