FCTC Test Test Firefighter Mathematical Problems 1

Question 1

A 100-foot section of 2.5-inch hose has a friction loss of 18 psi at a given flow rate. A firefighter extends the lay to 450 feet using the same hose and flow rate. What is the total friction loss in the extended hose?

Accepted Answer

81 psi

Answer

Friction loss is directly proportional to hose length. 450 feet is 4.5 times 100 feet, so total friction loss = 18 × 4.5 = 81 psi.

Question 2

A tanker carries 2,500 gallons of water to a rural fire scene. The attack crew is flowing at 125 GPM. Ignoring refill time, how many minutes will the tanker supply last?

Accepted Answer

20 minutes

Answer

Divide total water volume by flow rate: 2,500 ÷ 125 = 20 minutes.

Question 3

A firefighter must pump through 300 feet of 2.5-inch hose with a friction loss of 8 psi per 100 feet. The nozzle requires 80 psi nozzle pressure. What is the required pump discharge pressure?

Accepted Answer

104 psi

Answer

Total friction loss = 8 psi/100 ft × 3 sections = 24 psi. Pump discharge pressure = nozzle pressure + friction loss = 80 + 24 = 104 psi.

Question 4

A firefighter earns $35.00 per hour and works 56 hours in one week. Their contract pays overtime at 1.5 times the regular rate for hours beyond 40. What is their total gross pay for the week?

Accepted Answer

$2,240.00

Answer

Regular pay: 40 × $35 = $1,400. Overtime: 16 hours × ($35 × 1.5 = $52.50) = $840. Total: $1,400 + $840 = $2,240.

Question 5

Using the NFA fire flow formula (GPM = Length × Width ÷ 3), what is the required fire flow for a single-story commercial building measuring 75 feet by 120 feet?

Accepted Answer

3,000 GPM

Answer

Required flow = 75 × 120 ÷ 3 = 9,000 ÷ 3 = 3,000 GPM.

FCTC Test Practice Test

FCTC Test Practice Test

FCTC Test Test Firefighter Mathematical Problems 1