CPS Firefighter Test Firefighter Mathematical Reasoning Questions and Answers — Questions and Answers
Question 1: A fire engine is pumping water at a rate of 250 gallons per minute (GPM). If the fire requires an estimated 1,750 gallons of water to be extinguished, how many minutes will it take for the engine to deliver the necessary amount of water?
- 6 minutes
- 7 minutes (Correct answer)
- 8 minutes
- 5 minutes
Correct answer: 7 minutes
To determine the time required, divide the total number of gallons needed by the pumping rate. Calculation: 1,750 gallons / 250 gallons per minute = 7 minutes.
Question 2: According to safety guidelines, the base of a 28-foot ladder should be placed approximately one-quarter of its working length from the building. Which of the following is the correct distance?
- 6 feet
- 8 feet
- 7 feet (Correct answer)
- 9 feet
Correct answer: 7 feet
To find the correct distance, divide the ladder's length by 4. Calculation: 28 feet / 4 = 7 feet. The base of the ladder should be 7 feet from the building.
Question 3: A firefighter's SCBA cylinder contains 1,800 liters of air. The average consumption rate during heavy exertion is 80 liters per minute. After working for 12 minutes at this rate, how many liters of air will remain in the cylinder?
- 960 liters
- 1,040 liters
- 840 liters (Correct answer)
- 1,200 liters
Correct answer: 840 liters
First, calculate the total air consumed: 80 liters/minute * 12 minutes = 960 liters. Then, subtract the consumed air from the cylinder's total capacity: 1,800 liters - 960 liters = 840 liters remaining.
Question 4: A fire crew lays out 450 feet of a 2.5-inch hose. If the friction loss for this type of hose is 10 PSI per 100 feet, what is the total friction loss for the entire length of the hose?
- 40.5 PSI
- 45.0 PSI (Correct answer)
- 50.0 PSI
- 4500 PSI
Correct answer: 45.0 PSI
First, determine how many 100-foot sections are in the total length: 450 feet / 100 feet = 4.5 sections. Then, multiply the number of sections by the friction loss per section: 4.5 * 10 PSI = 45.0 PSI total friction loss.
Question 5: A fire engine's water tank has a capacity of 500 gallons. Knowing that water weighs approximately 8.34 pounds per gallon, what is the total weight of the water when the tank is full?
- 4,000 pounds
- 4,255 pounds
- 3,870 pounds
- 4,170 pounds (Correct answer)
Correct answer: 4,170 pounds
To find the total weight, multiply the volume of water in gallons by the weight per gallon. Calculation: 500 gallons * 8.34 pounds/gallon = 4,170 pounds.
Question 6: A fire inspector is checking a rectangular event space measuring 80 feet by 50 feet. The fire code mandates a maximum occupant load of one person for every 20 square feet. What is the maximum number of people legally allowed in this space?
- 250 people
- 130 people
- 200 people (Correct answer)
- 400 people
Correct answer: 200 people
First, calculate the total area of the space: 80 feet * 50 feet = 4,000 square feet. Next, divide the total area by the square footage required per person: 4,000 sq ft / 20 sq ft/person = 200 people.
CPS Firefighter Test Firefighter Mathematical Reasoning Questions and Answers
A fire engine is pumping water at a rate of 250 gallons per minute (GPM).
If the fire requires an estimated 1,750 gallons of water to be extinguished, how many minutes will it take for the engine to deliver the necessary amount of water?