FCTC Test Firefighter Mathematical Problems Questions and Answers 2 — Questions and Answers
Question 1: A pump is flowing 200 GPM at 150 psi. If the flow rate doubles to 400 GPM, approximately how does friction loss change? (Friction loss increases with the square of flow rate.)
- Doubles
- Triples
- Quadruples (Correct answer)
- Stays the same
Correct answer: Quadruples
Friction loss is proportional to flow rate squared. Doubling GPM from 200 to 400 gives a ratio of 2 squared equals 4, so friction loss quadruples.
Friction loss increases with the square of flow velocity and thus flow rate. Doubling GPM quadruples friction loss: (400 divided by 200) squared equals 4 times the original friction loss. This is why larger diameter hose is used for high-flow operations — larger diameter dramatically reduces friction loss.
Question 2: A building has three floors each 12 feet tall. What is the elevation pressure in psi that must be added to pump pressure? (Use 0.434 psi per foot)
- 10.0 psi
- 11.5 psi
- 13.0 psi
- 15.6 psi (Correct answer)
Correct answer: 15.6 psi
Total height equals 3 times 12 equals 36 feet; elevation pressure equals 36 times 0.434 equals 15.6 psi.
Elevation pressure compensates for the weight of the water column in the hose when operating above the pump. 36 feet times 0.434 psi per foot equals 15.6 psi must be added to pump discharge pressure to deliver adequate nozzle pressure on the third floor.
Question 3: A 2.5-inch hose carries 250 GPM total. A firefighter splits the flow equally into two 1.75-inch lines. How much does each line carry?
- 100 GPM
- 125 GPM (Correct answer)
- 150 GPM
- 200 GPM
Correct answer: 125 GPM
250 GPM divided by 2 equals 125 GPM per line.
When flow is split equally between two lines, each line receives half the total: 250 divided by 2 equals 125 GPM each. Engine operators performing wye operations must account for the split flow when calculating individual line friction loss and nozzle pressure requirements.
Question 4: A firefighter's hourly pay rate is $28.50. If they work a 24-hour shift, what is their gross pay for that shift?
- $570.00
- $684.00 (Correct answer)
- $712.00
- $750.00
Correct answer: $684.00
$28.50 multiplied by 24 hours equals $684.00.
$28.50 times 24 equals $684.00. Mathematical problems on firefighter exams often include pay calculations, scheduling, and resource allocation that require basic arithmetic. Accuracy with calculations is tested to assess attention to detail and numerical reasoning ability.
Question 5: The required fire flow for a 4,800 square foot building is calculated using the NFA formula: GPM equals area divided by 3. What is the required GPM?
- 800 GPM
- 1,200 GPM
- 1,600 GPM (Correct answer)
- 2,400 GPM
Correct answer: 1,600 GPM
4,800 divided by 3 equals 1,600 GPM.
The National Fire Academy fire flow formula estimates required GPM as floor area divided by 3 for a fully involved structure. 4,800 divided by 3 equals 1,600 GPM. This calculation helps incident commanders determine whether the on-scene water supply is adequate for suppression operations.
Question 6: A ladder is leaned against a wall using the 4:1 climbing angle rule (1 foot of base distance for every 4 feet of vertical height). If the top of the ladder is 16 feet high, how far from the wall is the base?
- 2 feet
- 4 feet (Correct answer)
- 8 feet
- 16 feet
Correct answer: 4 feet
Base distance equals vertical height divided by 4: 16 divided by 4 equals 4 feet.
The 4:1 rule positions the ladder base 1 foot away from the wall for every 4 feet of vertical height reached, producing approximately a 75-degree angle. 16 divided by 4 equals 4 feet. This angle provides safe climbing and good load-bearing stability for ground ladders.
FCTC Test Firefighter Mathematical Problems Questions and Answers 2
A pump is flowing 200 GPM at 150 psi.
If the flow rate doubles to 400 GPM, approximately how does friction loss change? (Friction loss increases with the square of flow rate.)