FCTC Numerical Reasoning 2 — Questions and Answers

Question 1: A fire engine travels 12 miles to a call at an average speed of 40 mph. How many minutes does it take to arrive?

15 minutes
18 minutes (Correct answer)
20 minutes
24 minutes

Correct answer: 18 minutes

Time = Distance ÷ Speed = 12 ÷ 40 = 0.3 hours = 0.3 × 60 = 18 minutes.

Using the formula Time = Distance ÷ Speed: 12 miles ÷ 40 mph = 0.3 hours. To convert to minutes: 0.3 × 60 = 18 minutes. This type of calculation appears frequently in FCTC numerical reasoning tests and relates to response time planning and apparatus deployment.

Question 2: A firefighter uses 400 gallons of water to suppress a fire. The fire engine tank holds 750 gallons. What percentage of the tank was used?

46.7%
50.0%
53.3% (Correct answer)
60.0%

Correct answer: 53.3%

400 ÷ 750 = 0.5333... = 53.3% (rounded to one decimal place).

To find the percentage used: (400 ÷ 750) × 100 = 53.33%. This rounds to 53.3%. Water supply management is a critical firefighting skill — knowing how much water remains in the tank at any point during an operation allows the pump operator and incident commander to call for resupply before the tank runs dry.

Question 3: Station A responds to 24 calls per week. Station B responds to 18 calls per week. How many more calls per year does Station A handle than Station B?

312 (Correct answer)
318
326
340

Correct answer: 312

Difference per week = 24 − 18 = 6 calls. Per year: 6 × 52 = 312 calls.

The weekly difference between the two stations is 24 − 18 = 6 calls. Over a year (52 weeks): 6 × 52 = 312 additional calls handled by Station A. This type of problem tests the ability to scale weekly figures to annual totals, a common requirement for budgeting, staffing analysis, and resource allocation in fire service administration.

Question 4: A hose delivers 150 gallons per minute. How many gallons are delivered in 7 minutes?

950
1,000
1,050 (Correct answer)
1,100

Correct answer: 1,050

150 gallons/min × 7 min = 1,050 gallons.

Flow calculations are fundamental to fireground hydraulics. At 150 gallons per minute (GPM), in 7 minutes the total water delivered is 150 × 7 = 1,050 gallons. Firefighters and pump operators use flow rate calculations to determine how long a tank supply will last, how many attack lines can be supported simultaneously, and whether the available water supply is sufficient for a given fire load.

Question 5: A crew of 4 firefighters completes a drill in 48 minutes. If the same workload is shared equally, how long would 6 firefighters take to complete the same drill?

24 minutes
28 minutes
30 minutes
32 minutes (Correct answer)

Correct answer: 32 minutes

Total work = 4 × 48 = 192 person-minutes. With 6 firefighters: 192 ÷ 6 = 32 minutes.

This is an inverse proportion problem. First calculate total person-minutes of work: 4 firefighters × 48 minutes = 192 person-minutes. If that same 192 person-minutes of work is split among 6 firefighters: 192 ÷ 6 = 32 minutes. This type of reasoning applies to tasks like laying hose, setting up ground ladders, and conducting searches where work can be divided among crew members.

Question 6: A building is 60 feet tall. A ladder must be placed at a 75-degree climbing angle. Approximately how far from the base of the building should the foot of the ladder be placed?

8 feet
14 feet
16 feet (Correct answer)
22 feet

Correct answer: 16 feet

At 75°, the horizontal distance ≈ height × tan(15°) ≈ 60 × 0.268 ≈ 16 feet. Alternatively, the 1-in-4 rule gives 60÷4 = 15 ft, closest to 16 ft.

The fire service uses the 1-in-4 rule for ladder placement: the base of the ladder should be placed 1 foot away from the wall for every 4 feet of ladder height. For a 60-foot building: 60 ÷ 4 = 15 feet. The answer option closest to this is 16 feet. Mathematically, at 75°, tan(75°) ≈ 3.73, so the opposite side (height) = adjacent (base) × 3.73, giving base = 60 ÷ 3.73 ≈ 16.1 feet, confirming this answer.

FCTC Numerical Reasoning 2

A fire engine travels 12 miles to a call at an average speed of 40 mph.
How many minutes does it take to arrive?