FCTC Test Firefighter Mathematical Problems Questions and Answers 1 — Questions and Answers
Question 1: An engine is supplying two separate attack lines to fight a fire. Attack Line 1 is flowing 150 GPM and Attack Line 2 is flowing 125 GPM. What is the total gallons per minute (GPM) being discharged from the pumper for these two lines?
- 250 GPM
- 275 GPM (Correct answer)
- 225 GPM
- 300 GPM
Correct answer: 275 GPM
The total GPM being discharged is the sum of the flow rates from each individual line. To find the answer, add the GPM of Attack Line 1 to the GPM of Attack Line 2: 150 GPM + 125 GPM = 275 GPM.
Question 2: A firefighter is calculating the friction loss in a 300-foot section of 2.5-inch hose flowing 200 GPM. Using the formula: FL = C × (GPM/100)² × (L/100), where the coefficient (C) for this hose is 2. What is the total friction loss in PSI?
- 12 PSI
- 18 PSI
- 24 PSI (Correct answer)
- 30 PSI
Correct answer: 24 PSI
First, calculate the terms in the parentheses: (200/100) = 2, and (300/100) = 3. Then, square the GPM term as indicated by the formula: 2² = 4. Finally, multiply all the parts together: FL = 2 × 4 × 3 = 24 PSI.
Question 3: A fire engine is using its 500-gallon water tank to extinguish a car fire. If the attack line is flowing at a constant rate of 100 gallons per minute (GPM), how many minutes will the water tank last before it is empty?
- 4 minutes
- 4.5 minutes
- 6 minutes
- 5 minutes (Correct answer)
Correct answer: 5 minutes
To find the duration, divide the total volume of water in the tank by the flow rate of the hose line. Calculation: 500 gallons / 100 gallons per minute = 5 minutes.
Question 4: A crew is assigned to perform salvage and cover the floor of a rectangular retail space to protect it from water damage. The room measures 30 feet wide by 50 feet long. What is the total square footage of the floor that the crew must cover?
- 1,500 square feet (Correct answer)
- 80 square feet
- 1,600 square feet
- 1,200 square feet
Correct answer: 1,500 square feet
The area of a rectangle is calculated by multiplying its length by its width. In this scenario, the calculation is: Area = 50 feet × 30 feet = 1,500 square feet.
Question 5: A firefighter must place a 28-foot extension ladder against a building to reach a third-story window. The base of the window is 24 feet from the ground. Using the standard 4:1 ratio for a safe climbing angle (ladder base should be 1 foot from the building for every 4 feet of vertical height), what is the correct distance from the building to place the base of the ladder?
- 7 feet
- 5 feet
- 8 feet
- 6 feet (Correct answer)
Correct answer: 6 feet
The calculation for ladder setback is based on the vertical working height the ladder reaches, not its total length. Using the 4:1 ratio, divide the vertical height (24 feet) by 4. Calculation: 24 feet / 4 = 6 feet. The base of the ladder should be placed 6 feet away from the building.
Question 6: A firefighter starts an operation with a 4500 PSI SCBA cylinder. After 10 minutes of work, the pressure gauge reads 3000 PSI. Assuming a constant rate of air consumption, how many more minutes can the firefighter work before the cylinder pressure drops to the 1500 PSI reserve level where they must begin exiting?
- 15 minutes
- 10 minutes (Correct answer)
- 12 minutes
- 8 minutes
Correct answer: 10 minutes
1. Calculate pressure used: 4500 PSI (start) - 3000 PSI (current) = 1500 PSI used. 2. Calculate consumption rate: 1500 PSI was used in 10 minutes, so the rate is 1500 PSI / 10 min = 150 PSI per minute. 3. Calculate usable air remaining before the reserve: 3000 PSI (current) - 1500 PSI (reserve) = 1500 PSI of usable air. 4. Calculate remaining time: 1500 PSI (usable air) / 150 PSI per minute (rate) = 10 minutes.
FCTC Test Firefighter Mathematical Problems Questions and Answers 1
An engine is supplying two separate attack lines to fight a fire.
Attack Line 1 is flowing 150 GPM and Attack Line 2 is flowing 125 GPM.
What is the total gallons per minute (GPM) being discharged from the pumper for these two lines?