Firefighter Mathematical Reasoning 1 Flashcards

A firefighter's protective gear weighs 45 pounds. If a full crew of 8 firefighters suits up for a call, what is the total combined weight of all gear?

Answer: 360 lbs

Multiply the weight per person by the number of crew members: 45 × 8 = 360 pounds total.

A fire station's onboard water tank holds 750 gallons. If the hose discharges water at 150 gallons per minute, how many minutes will the tank last?

Answer: 5 minutes

Divide total capacity by the discharge rate: 750 ÷ 150 = 5 minutes until the tank is empty.

A fire department has 120 active personnel. If 15% are currently on medical or administrative leave, how many firefighters are on duty?

Answer: 102

15% of 120 = 18 firefighters on leave. 120 − 18 = 102 firefighters on active duty.

Firefighter training sessions run 6 hours per day for 5 days. If 3 training sessions are held in a single month, how many total training hours are logged?

Answer: 90 hours

Each session = 6 hours × 5 days = 30 hours. Three sessions = 30 × 3 = 90 total hours.

A fire truck traveling to an emergency covers 12 miles at an average speed of 36 mph. How many minutes does the response take?

Answer: 20 minutes

Time = distance ÷ speed = 12 ÷ 36 = 1/3 hour. Converting to minutes: 1/3 × 60 = 20 minutes.

A ladder is leaned against a building with its base 6 feet from the wall and it reaches exactly 8 feet up the wall. What is the length of the ladder?

Answer: 10 ft

Use the Pythagorean theorem: ladder² = 6² + 8² = 36 + 64 = 100. √100 = 10 feet.