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FCTC Firefighter Math Applications 1 Flashcards

6 cards from real FCTC practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  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?

    Answer: 1,800 gallons

    Add both flow rates: 125 + 175 = 300 GPM combined. Multiply by time: 300 × 6 = 1,800 gallons total discharged.

  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?

    Answer: 180 gallons

    Water used = 80 GPM × 4 minutes = 320 gallons. Remaining = 500 − 320 = 180 gallons.

  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?

    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.

  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?

    Answer: 31.25%

    Divide active time by total shift time and multiply by 100: (7.5 ÷ 24) × 100 = 31.25%.

  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?

    Answer: 10 minutes

    Divide the total volume by the flow rate: 3,000 ÷ 300 = 10 minutes to fill the tanker.

  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?

    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.