FCTC Test Test Firefighter Mathematical Problems 1 — Questions and Answers
Question 1: A 100-foot section of 2.5-inch hose has a friction loss of 18 psi at a given flow rate. A firefighter extends the lay to 450 feet using the same hose and flow rate. What is the total friction loss in the extended hose?
- 36 psi
- 54 psi
- 81 psi (Correct answer)
- 90 psi
Correct answer: 81 psi
Friction loss is directly proportional to hose length. 450 feet is 4.5 times 100 feet, so total friction loss = 18 × 4.5 = 81 psi.
Question 2: A tanker carries 2,500 gallons of water to a rural fire scene. The attack crew is flowing at 125 GPM. Ignoring refill time, how many minutes will the tanker supply last?
- 12 minutes
- 16 minutes
- 20 minutes (Correct answer)
- 25 minutes
Correct answer: 20 minutes
Divide total water volume by flow rate: 2,500 ÷ 125 = 20 minutes.
Question 3: A firefighter must pump through 300 feet of 2.5-inch hose with a friction loss of 8 psi per 100 feet. The nozzle requires 80 psi nozzle pressure. What is the required pump discharge pressure?
- 88 psi
- 96 psi
- 104 psi (Correct answer)
- 112 psi
Correct answer: 104 psi
Total friction loss = 8 psi/100 ft × 3 sections = 24 psi. Pump discharge pressure = nozzle pressure + friction loss = 80 + 24 = 104 psi.
Question 4: A firefighter earns $35.00 per hour and works 56 hours in one week. Their contract pays overtime at 1.5 times the regular rate for hours beyond 40. What is their total gross pay for the week?
- $1,960.00
- $2,100.00
- $2,240.00 (Correct answer)
- $2,940.00
Correct answer: $2,240.00
Regular pay: 40 × $35 = $1,400. Overtime: 16 hours × ($35 × 1.5 = $52.50) = $840. Total: $1,400 + $840 = $2,240.
Question 5: Using the NFA fire flow formula (GPM = Length × Width ÷ 3), what is the required fire flow for a single-story commercial building measuring 75 feet by 120 feet?
- 1,500 GPM
- 2,400 GPM
- 3,000 GPM (Correct answer)
- 4,500 GPM
Correct answer: 3,000 GPM
Required flow = 75 × 120 ÷ 3 = 9,000 ÷ 3 = 3,000 GPM.
Question 6: An engine company pumps at a steady 350 GPM for 30 minutes while suppressing a structure fire. How many total gallons of water did the engine discharge?
- 3,500 gallons
- 7,000 gallons
- 10,500 gallons (Correct answer)
- 14,000 gallons
Correct answer: 10,500 gallons
Total gallons = flow rate × time = 350 GPM × 30 minutes = 10,500 gallons.
FCTC Test Test Firefighter Mathematical Problems 1
A 100-foot section of 2.5-inch hose has a friction loss of 18 psi at a given flow rate.
A firefighter extends the lay to 450 feet using the same hose and flow rate.
What is the total friction loss in the extended hose?