Free FCTC Test Firefighter Mathematical Problems Questions and Answers — Questions and Answers
Question 1: An engine company must provide water for an offensive fire attack using two handlines. The first handline is flowing at a rate of 150 gallons per minute (GPM), and the second handline is flowing at 175 GPM. What is the total flow rate in GPM that the pump operator must supply for both lines?
- 275 GPM
- 300 GPM
- 325 GPM (Correct answer)
- 350 GPM
Correct answer: 325 GPM
To find the total flow rate required, the pump operator must add the flow rates of each individual hoseline. The calculation is 150 GPM + 175 GPM = 325 GPM.
Question 2: A fire engine's water tank has a capacity of 500 gallons. If it is being refilled from a hydrant at a steady rate of 125 gallons per minute (GPM), how many minutes will it take to fill the tank from empty to full?
- 4 minutes (Correct answer)
- 3.5 minutes
- 4.5 minutes
- 5 minutes
Correct answer: 4 minutes
To determine the time required to fill the tank, divide the total capacity of the tank by the rate at which it is being filled. The calculation is 500 gallons / 125 GPM = 4 minutes.
Question 3: A fire crew is laying out four 100-foot sections of 2.5-inch hose. What is the total length of the hose lay in feet?
- 300 feet
- 400 feet (Correct answer)
- 500 feet
- 250 feet
Correct answer: 400 feet
This is a multiplication problem. To find the total length, multiply the number of sections by the length of each section. The calculation is 4 sections × 100 feet/section = 400 feet.
Question 4: A firefighter needs to calculate the floor area of a room to determine ventilation requirements. The room is rectangular and measures 40 feet in length by 25 feet in width. What is the total area of the room in square feet?
- 800 square feet
- 950 square feet
- 1,000 square feet (Correct answer)
- 1,250 square feet
Correct answer: 1,000 square feet
The area of a rectangle is calculated by multiplying its length by its width. The calculation is 40 feet × 25 feet = 1,000 square feet.
Question 5: A 50-foot section of 2.5-inch fire hose, when full, contains approximately 13 gallons of water. Knowing that water weighs about 8.34 pounds per gallon, what is the approximate weight of the water inside two full sections of this hose?
- 108 lbs
- 217 lbs (Correct answer)
- 260 lbs
- 167 lbs
Correct answer: 217 lbs
First, calculate the total volume of water in two sections: 2 sections × 13 gallons/section = 26 gallons. Then, multiply the total gallons by the weight of water per gallon: 26 gallons × 8.34 lbs/gallon ≈ 216.84 lbs, which rounds to 217 lbs.
Question 6: A hydraulic rescue tool operates at a pressure of 5,000 pounds per square inch (PSI). If the tool's piston has a surface area of 4 square inches, what is the total amount of force the tool can generate?
- 1,250 pounds
- 5,004 pounds
- 10,000 pounds
- 20,000 pounds (Correct answer)
Correct answer: 20,000 pounds
Force is calculated by multiplying pressure by the area over which it is applied (Force = Pressure × Area). The calculation is 5,000 PSI × 4 square inches = 20,000 pounds of force.
Free FCTC Test Firefighter Mathematical Problems Questions and Answers
An engine company must provide water for an offensive fire attack using two handlines.
The first handline is flowing at a rate of 150 gallons per minute (GPM), and the second handline is flowing at 175 GPM.
What is the total flow rate in GPM that the pump operator must supply for both lines?