Firefighting Math Problems and Solutions, Exams of Applied Mathematics

A collection of math problems related to firefighting scenarios, providing solutions for each problem. It covers various aspects of firefighting, including water tank capacity, hose length calculations, pressure calculations, and vehicle speed calculations. The problems are designed to test understanding of basic math concepts and their application in firefighting contexts.

Typology: Exams

2024/2025

Available from 04/16/2025

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FCTC Math questions with correct
solutions
Average money for dinner - CORRECT ANSWERS โœ”โœ”$14.29
How many 2 pints will fit in a 5 gallon drum? - CORRECT ANSWERS
โœ”โœ”20 pints
Fire increase between 2009-2014? - CORRECT ANSWERS โœ”โœ”145%
Total chains crew cuts - CORRECT ANSWERS โœ”โœ”6
Total cost 12.4+14.2+14.4+12.2 - CORRECT ANSWERS โœ”โœ”53.2
7ft length 5 ft wife and 3ft deep, how much water can be held in engine
17's water tank? - CORRECT ANSWERS โœ”โœ”105 cubic ft
A tank with 12' diameter holds 864 gallons per foot of depth, how many
gallons will a tank with 12' diameter hold if it is 5' deep? - CORRECT
ANSWERS โœ”โœ”4320
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FCTC Math questions with correct

solutions

Average money for dinner - CORRECT ANSWERS โœ”โœ” $14. How many 2 pints will fit in a 5 gallon drum? - CORRECT ANSWERS โœ”โœ” 20 pints Fire increase between 2009-2014? - CORRECT ANSWERS โœ”โœ” 145% Total chains crew cuts - CORRECT ANSWERS โœ”โœ” 6 Total cost 12.4+14.2+14.4+12.2 - CORRECT ANSWERS โœ”โœ” 53. 7ft length 5 ft wife and 3ft deep, how much water can be held in engine 17's water tank? - CORRECT ANSWERS โœ”โœ” 105 cubic ft A tank with 12' diameter holds 864 gallons per foot of depth, how many gallons will a tank with 12' diameter hold if it is 5' deep? - CORRECT ANSWERS โœ”โœ” 4320

Engine 33 is traveling 351 miles to a mutual aid. They have to drive 216 miles in 4 hours, what is their average speed? - CORRECT ANSWERS โœ”โœ” 54mph There are 6 sections of 100' Wildland hose and 9 sections of 80' structural hose. 5 sections of structural hose fail. What is the total amount of structural hose that failed? - CORRECT ANSWERS โœ”โœ” 400ft Engine carries 1,100 ft of 2 1/2 inch, 900ft of 4 inch and 1,000ft of 4 1/2 in; if the 4 inch was removed, what percentage was removed? - CORRECT ANSWERS โœ”โœ” 30% For a fire on the fourth floor, you need 100 psi at the nozzle, for each floor above the first floor you lose 5 psi, for every 100ft of hose you lose 15 psi. There is 400ft of hose used to get to the fire, what is the total pressure needed at the engine? - CORRECT ANSWERS โœ”โœ” 175 psi Engine pumps 1450 gallons per minute, how many gallons will it pump in 5 1/2 min? - CORRECT ANSWERS โœ”โœ” 7,975 gallons If an acre is equal to 43,560 square ft and a fire burned 250ft wide and 1,200ft long, how many acres were burned? - CORRECT ANSWERS โœ”โœ” 6.88 Acres 1/4 of back burned, 1/4 of front burned, 1/3 of her head burned, 1/2 of her armed burned. What is the percentage of the total burn?

Residential floors are typically 12 ft high. The window sill is 4 ft above the floor. It's standard to have top of ladder 4 ft above window sill or roof. What is the minimum ladder height required for a 2 story window? - CORRECT ANSWERS โœ”โœ” 24 ft ladder If engine 1 is responding to a call 4. miles away and has an average speed of 50 mph and engine 2 is responding to the same call and has to go 6 miles with and average speed of 55 mph. Who will be on scene first and by how much time? - CORRECT ANSWERS โœ”โœ” Engine 1 by 1 minute and 9 seconds You and your crew are buying dinner, there are 7 of you. Each person chips in $9. Dinner costs $64.44 - CORRECT ANSWERS โœ”โœ” Over $1. What two vehicles would fit in the app bay if they were stacked on each other? - CORRECT ANSWERS โœ”โœ” Squad 23ft and battalion 9 15ft Boys and girls get 60 votes for class president. A ratio 3:2. How many votes do boys get? - CORRECT ANSWERS โœ”โœ” Boys 36 girls 24 3 different sizes of horse. You are given the total amount of hose, total, but you have to determine how much that was used? - CORRECT ANSWERS โœ”โœ” 700ft

66 feet in a chain, on average a firefighter can cut 10 chains in an hour. How many yards can he cut in an hour? - CORRECT ANSWERS โœ”โœ” 220 yards Tank 1. 830 gallons x 2ft depth = 1660 Tank 2. 670 gallons x 2ft depth = 1340 - CORRECT ANSWERS โœ”โœ” 330 You have an 8 gallon tank you have to fill. Each bottle is 2.5 gallons. How many is required to fill the 8 gallon - CORRECT ANSWERS โœ”โœ” 3. The one about the engine pump. The tank holds 500 gallons. How much time do you have left in 90 seconds if you are flowing at 125 gpm? - CORRECT ANSWERS โœ”โœ” 150 seconds Engine 1 has a tank that hold 40 gal tank and gets 15mpg. While engine 2 tank hold 35 gallons and get 17mpg. Which engine will go further and which engine will run out of fuel first? - CORRECT ANSWERS โœ”โœ” Engine 2 will go 5 miles less than Engine 1 and Engine 1 will run out of fuel first Class K Fire Extinguisher needs to be 30 feet from the farthest cooking device and near the next door, stove is 20ft from the door. Pizza oven is 40ft from the door and the fryer is 25ft from door. Where does the extinguisher need to be placed? - CORRECT ANSWERS โœ”โœ” 25 ft

L111 gets 4 miles per gallon. If L111 drives 76 miles how many gallons of diesel will it have used? Round to the nearest whole number. - CORRECT ANSWERS โœ”โœ” 19 If gas costs $3.29 per gallon and you purchase 6.5 gallons, how much money will you spend? - CORRECT ANSWERS โœ”โœ” $21. Engine 5 has a fell water tank that holds 100 gallons, Engine 7 holds 1, gallons of water and is full. With a total of three hose lines flowing, each at 125 gpm on a fully involved barn fire. How many 3,500 gallon water tenders would be required to sustain this operation for 1.5 hours? - CORRECT ANSWERS โœ”โœ” 9 Water tenders including engine 5 and engine 7 Engine 19 travels 5.45 gpm. They traveled 185 miles. How many gallons did they use? - CORRECT ANSWERS โœ”โœ” 33 (33.94) Formula for determining the head pressure difference between and intake and output - CORRECT ANSWERS โœ”โœ” 1 vertical foot = 0.433psi 1psi = 2.31 vertical feet If engine 1 has a 40 gallon tank and gets 15 miles per gallon and engine 2 has a 35 gallon tank and gets 17 miles per gallon, both engines go the same distance, which engine will run out of fuel first and which engine would drive further? - CORRECT ANSWERS โœ”โœ” Engine 1 will run out of fuel first and go 5 miles more than Engine 2