FCTC Test Firefighter Mathematical Problems 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?

Accepted Answer

275 GPM

Answer

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?

Accepted Answer

24 PSI

Answer

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?

Accepted Answer

5 minutes

Answer

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?

Accepted Answer

1,500 square feet

Answer

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?

Accepted Answer

6 feet

Answer

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.

FCTC Test Practice Test

FCTC Test Practice Test

FCTC Test Firefighter Mathematical Problems Questions and Answers