FCTC Firefighter Math Applications Questions and Answers — Questions and Answers
Question 1: An engine company is operating two attack lines at a residential fire. The first line is a 1.75-inch hose flowing 150 gallons per minute (GPM). The second line is a 2.5-inch hose flowing 250 GPM. What is the total flow rate, in GPM, that the pump operator must supply to maintain pressure for both lines?
- 350 GPM
- 400 GPM (Correct answer)
- 300 GPM
- 450 GPM
Correct answer: 400 GPM
To find the total flow rate required from the pump, simply add the flow rates of each individual hoseline being supplied. In this case, 150 GPM (Line 1) + 250 GPM (Line 2) equals a total of 400 GPM.
Question 2: A firefighter is operating a 2.5-inch hoseline that is 300 feet long and is flowing 250 GPM. Using a common fireground rule of thumb that estimates friction loss in 2.5-inch hose at this flow rate to be approximately 15 psi per 100 feet, what is the TOTAL estimated friction loss for the entire hoseline?
- 15 psi
- 30 psi
- 45 psi (Correct answer)
- 60 psi
Correct answer: 45 psi
The rule of thumb states a friction loss of 15 psi for every 100 feet of hose. Since the total length is 300 feet, you multiply the friction loss per section by the number of sections (300 feet / 100 feet = 3 sections). Therefore, 15 psi/section * 3 sections = 45 psi total friction loss.
Question 3: You are the pump operator supplying an attack line to the 5th floor of an apartment building. The firefighting crew is using a standard fog nozzle that requires 100 psi nozzle pressure. The friction loss in the 200 feet of 1.75-inch hose is calculated to be 40 psi. You must also account for head loss, which is approximately 5 psi for each floor above the fire engine. What is the correct Pump Discharge Pressure (PDP)?
- 140 psi
- 145 psi
- 125 psi
- 160 psi (Correct answer)
Correct answer: 160 psi
The formula for Pump Discharge Pressure is PDP = Nozzle Pressure (NP) + Total Friction Loss (FL) + Elevation (Head) Loss. Head loss is 5 psi per floor above the engine, so for the 5th floor, it's 4 floors up (5-1=4), which is 4 * 5 psi = 20 psi. Therefore, PDP = 100 psi (NP) + 40 psi (FL) + 20 psi (Head Loss) = 160 psi.
Question 4: A hazardous materials incident has occurred in a sealed warehouse room. To properly ventilate the space, you must first calculate its total volume. The room measures 40 feet long, 30 feet wide, and has a ceiling height of 20 feet. What is the volume of the room in cubic feet?
- 24,000 cubic feet (Correct answer)
- 1,200 cubic feet
- 90 cubic feet
- 7,200 cubic feet
Correct answer: 24,000 cubic feet
The volume of a rectangular space is calculated by multiplying its length by its width by its height. In this scenario, the calculation is 40 ft (Length) x 30 ft (Width) x 20 ft (Height) = 24,000 cubic feet.
Question 5: A 3,000-gallon water tender is being used in a shuttle operation to supply water to a rural fire scene. The total time for one complete cycle (drive to the scene, dump the water, return to the fill site, and refill the tank) is 20 minutes. How many total gallons of water can this tender deliver to the scene in one hour?
- 3,000 gallons
- 6,000 gallons
- 9,000 gallons (Correct answer)
- 12,000 gallons
Correct answer: 9,000 gallons
First, determine how many trips the tender can make in one hour (60 minutes). With a cycle time of 20 minutes, the tender can complete 60 minutes / 20 minutes/cycle = 3 cycles. Then, multiply the number of cycles by the tender's capacity: 3 cycles * 3,000 gallons/cycle = 9,000 gallons.
Question 6: Your fire engine has a 750-gallon water tank. After extinguishing a car fire, you notice that the tank level reading shows you have 600 gallons remaining. What percentage of the total water capacity did you use?
- 15%
- 80%
- 25%
- 20% (Correct answer)
Correct answer: 20%
First, calculate the amount of water used: 750 gallons (start) - 600 gallons (remaining) = 150 gallons used. Next, to find the percentage used, divide the amount used by the total capacity and multiply by 100: (150 gallons used / 750 gallons total) * 100 = 0.20 * 100 = 20%.
FCTC Firefighter Math Applications Questions and Answers
An engine company is operating two attack lines at a residential fire.
The first line is a 1.75-inch hose flowing 150 gallons per minute (GPM).
The second line is a 2.5-inch hose flowing 250 GPM.
What is the total flow rate, in GPM, that the pump operator must supply to maintain pressure for both lines?