FCTC Test FCTC Firefighter Math Applications 1 — Questions and Answers
Question 1: Two hose lines are operating simultaneously at a structure fire. Line A flows 125 GPM and Line B flows 175 GPM. How many total gallons are discharged after 6 minutes?
- 1,200 gallons
- 1,500 gallons
- 1,800 gallons (Correct answer)
- 2,100 gallons
Correct answer: 1,800 gallons
Add both flow rates: 125 + 175 = 300 GPM combined. Multiply by time: 300 × 6 = 1,800 gallons total discharged.
Question 2: A fire engine's water tank holds 500 gallons. The engine pumps at 80 GPM for 4 minutes before a water supply is established. How many gallons remain in the tank?
- 80 gallons
- 180 gallons (Correct answer)
- 320 gallons
- 420 gallons
Correct answer: 180 gallons
Water used = 80 GPM × 4 minutes = 320 gallons. Remaining = 500 − 320 = 180 gallons.
Question 3: A ground ladder must reach the roof of a 60-foot building. The base of the ladder is placed 15 feet from the building wall. Using the Pythagorean theorem (c² = a² + b²), what is the minimum ladder length needed?
- Approximately 55 feet
- Approximately 58 feet
- Approximately 62 feet (Correct answer)
- Approximately 75 feet
Correct answer: Approximately 62 feet
c² = 60² + 15² = 3,600 + 225 = 3,825. √3,825 ≈ 61.8 feet, so a ladder of at least 62 feet is required.
Question 4: A fire crew works a 24-hour shift and spends a total of 7.5 hours on active structure-fire operations. What percentage of the shift was spent on structure fires?
- 25.5%
- 31.25% (Correct answer)
- 37.5%
- 42%
Correct answer: 31.25%
Divide active time by total shift time and multiply by 100: (7.5 ÷ 24) × 100 = 31.25%.
Question 5: A pump operator needs to fill a tanker truck that holds 3,000 gallons. The pump discharges water at 300 GPM. How many minutes will it take to fill the tanker?
- 6 minutes
- 8 minutes
- 10 minutes (Correct answer)
- 12 minutes
Correct answer: 10 minutes
Divide the total volume by the flow rate: 3,000 ÷ 300 = 10 minutes to fill the tanker.
Question 6: Each hose section at a fire station is 50 feet long. A firefighter needs to stretch a line to a point 220 feet from the engine. How many hose sections are required to reach the target?
- 3 sections
- 4 sections
- 5 sections (Correct answer)
- 6 sections
Correct answer: 5 sections
Divide the required distance by section length: 220 ÷ 50 = 4.4 sections. Since partial sections cannot be used, 5 full sections are needed to reach 220 feet.
FCTC Test FCTC Firefighter Math Applications 1
Two hose lines are operating simultaneously at a structure fire.
Line A flows 125 GPM and Line B flows 175 GPM.
How many total gallons are discharged after 6 minutes?