Free CPS Firefighter Test Firefighter Mathematical Reasoning Questions and Answers — Questions and Answers
Question 1: A fire engine's water tank holds 500 gallons. If the crew is attacking a fire with a hoseline flowing at 125 gallons per minute (GPM), how many minutes will the tank's water supply last?
- 4 minutes (Correct answer)
- 5 minutes
- 3.5 minutes
- 6 minutes
Correct answer: 4 minutes
To determine how long the water supply will last, divide the total volume of water in the tank by the flow rate of the hoseline. 500 gallons / 125 GPM = 4 minutes.
Question 2: A firefighter must carry two 50-foot sections of 1.75-inch hose up three flights of stairs. If each 50-foot section weighs 28 pounds when empty, what is the total weight of the hose the firefighter is carrying?
- 28 pounds
- 84 pounds
- 56 pounds (Correct answer)
- 112 pounds
Correct answer: 56 pounds
The question asks for the total weight of the two sections of hose being carried. Multiply the weight of one section by the number of sections: 28 pounds/section * 2 sections = 56 pounds. The number of stairs is extra information not needed for the calculation.
Question 3: A fire has occurred in a rectangular room that measures 50 feet long by 30 feet wide. What is the total square footage of the room?
- 1,200 square feet
- 80 square feet
- 1,600 square feet
- 1,500 square feet (Correct answer)
Correct answer: 1,500 square feet
To find the area of a rectangle, you multiply its length by its width. In this case, 50 feet * 30 feet = 1,500 square feet.
Question 4: An engine company is dispatched to a call 9 miles away. If the engine travels at an average speed of 36 miles per hour, how many minutes will it take to arrive at the scene?
- 20 minutes
- 15 minutes (Correct answer)
- 4 minutes
- 25 minutes
Correct answer: 15 minutes
First, calculate the travel time in hours by dividing the distance by the speed (Time = Distance / Speed). So, 9 miles / 36 mph = 0.25 hours. To convert hours to minutes, multiply by 60: 0.25 * 60 = 15 minutes.
Question 5: A firefighter needs to use a 3% foam concentrate to extinguish a flammable liquid fire. If the total amount of foam solution needed is 150 gallons, how many gallons of foam concentrate are required?
- 3 gallons
- 5 gallons
- 4.5 gallons (Correct answer)
- 1.5 gallons
Correct answer: 4.5 gallons
To calculate the amount of foam concentrate, convert the percentage to a decimal (3% = 0.03) and multiply it by the total solution volume. 150 gallons * 0.03 = 4.5 gallons.
Question 6: A ladder must be raised to a window that is 24 feet above the ground. To be placed at the proper angle, the base of the ladder should be 7 feet away from the building. What is the minimum length the ladder must be to reach the window?
- 25 feet (Correct answer)
- 31 feet
- 23 feet
- 28 feet
Correct answer: 25 feet
This problem forms a right triangle and can be solved using the Pythagorean theorem (a² + b² = c²). The height (24 feet) and the distance from the building (7 feet) are the legs. So, 24² + 7² = c². This becomes 576 + 49 = c², which equals 625. The square root of 625 is 25. Therefore, the ladder must be at least 25 feet long.
Free CPS Firefighter Test Firefighter Mathematical Reasoning Questions and Answers
A fire engine's water tank holds 500 gallons.
If the crew is attacking a fire with a hoseline flowing at 125 gallons per minute (GPM), how many minutes will the tank's water supply last?