FCTC Firefighter Math Applications 5 — Questions and Answers
Question 1: A warehouse measures 120 feet × 80 feet. Fire code requires 1 sprinkler head per 144 square feet. How many sprinkler heads are needed?
- 55
- 60
- 66 (Correct answer)
- 67
Correct answer: 66
Area = 120 × 80 = 9,600 sq ft; 9,600 ÷ 144 = 66.67, rounded up to 67… so correct answer is 67.
Question 2: A department purchased 6 sets of turnout gear at $1,850 each and 6 SCBAs at $3,200 each. What was the total equipment cost?
- $28,500
- $30,300 (Correct answer)
- $30,800
- $31,200
Correct answer: $30,300
(6 × $1,850) + (6 × $3,200) = $11,100 + $19,200 = $30,300.
Question 3: A fire crew must drain a flooded basement holding 4,500 gallons. Their pump removes 75 gallons per minute. How long will it take to drain the basement?
- 50 minutes
- 55 minutes
- 60 minutes (Correct answer)
- 65 minutes
Correct answer: 60 minutes
4,500 ÷ 75 = 60 minutes.
Question 4: Engine 3 uses 12 gallons of diesel fuel per hour. If the tank holds 60 gallons and starts full, how long can it run before refueling?
- 3 hours
- 4 hours
- 5 hours (Correct answer)
- 6 hours
Correct answer: 5 hours
60 ÷ 12 = 5 hours of operation.
Question 5: During a wildland fire, a crew constructs a firebreak at a rate of 200 feet per hour. If the fire is 1.5 miles away and traveling at 400 feet per hour, how many hours does the crew have before the fire arrives?
- 10.56 hours
- 11.88 hours
- 19.8 hours (Correct answer)
- 21.12 hours
Correct answer: 19.8 hours
1.5 miles = 7,920 feet; 7,920 ÷ 400 ft/hr = 19.8 hours.
Question 6: A fire report shows 12 structure fires, 8 vehicle fires, and 20 medical assists in one month. What percentage of total calls were structure fires?
- 25%
- 30% (Correct answer)
- 33%
- 40%
Correct answer: 30%
Total = 12 + 8 + 20 = 40; 12 ÷ 40 × 100 = 30%.
Question 7: A nozzle tip with a 1.5-inch diameter is replaced with one of 1-inch diameter. If flow rate is proportional to the cross-sectional area, by approximately what percentage does flow decrease?
- 33%
- 44%
- 55% (Correct answer)
- 67%
Correct answer: 55%
Area ratio = (1²) ÷ (1.5²) = 1 ÷ 2.25 ≈ 0.444; decrease = 1 - 0.444 ≈ 55.6%.
FCTC Firefighter Math Applications 5
A warehouse measures 120 feet × 80 feet.
Fire code requires 1 sprinkler head per 144 square feet.
How many sprinkler heads are needed?