Firefighter Math — Question Explanations
Firefighter entrance math — arithmetic, fractions, decimals, percentages, ratios, conversions, hydraulics-style word problems.
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What is 3/4 of 120?
To find 3/4 of 120, multiply 120 by 3/4: (3/4) * 120 = 90. The correct answer is "90". This reflects the accepted standard for the firefighter-math assessment a
A firefighter spent $45 on new gloves and $25 on a new helmet light. What was the total cost?
Add the two costs together: $45 + $25 = $70. The correct answer is "$70". This reflects the accepted standard for the firefighter-math assessment and aligns wit
Friction loss formula commonly used: FL = C × Q^2 × L. For a 1¾'' line (C=15.5), Q=1.5 (150 GPM in hundreds…
FL = 15.5 × 1.5^2 × 2 = 15.5 × 2.25 × 2 = 69.75 ≈ 70 psi. The correct answer is "~70 psi". This reflects the accepted standard for the firefighter-math assessme
Pump flows 250 GPM. To deliver 5,000 gallons takes:
5000 ÷ 250 = 20 minutes. The correct answer is "20 min". This reflects the accepted standard for the firefighter-math assessment and aligns with the official ha
To mix a 3% foam solution in 200 gallons of water, how much foam concentrate is needed?
3% × 200 = 6 gallons of foam concentrate. The correct answer is "6 gal". This reflects the accepted standard for the firefighter-math assessment and aligns with
A cylindrical tank radius 2 m, height 3 m. Volume (π≈3.14):
V = π r² h = 3.14 × 4 × 3 ≈ 37.7 m³. The correct answer is "~37.7 m³". This reflects the accepted standard for the firefighter-math assessment and aligns with t
A hose flows at 150 GPM for 4 minutes. Total water delivered:
150 × 4 = 600 gallons. The correct answer is "600 gal". This reflects the accepted standard for the firefighter-math assessment and aligns with the official han
Area of a rectangular room 12 ft × 15 ft:
Area = L × W = 12 × 15 = 180 sq ft. The correct answer is "180 sq ft". This reflects the accepted standard for the firefighter-math assessment and aligns with t
What is 15% of 300?
To find 15% of 300, convert the percentage to a decimal (0.15) and multiply: 0.15 * 300 = 45.
The average response time to an incident is 7 minutes and 30 seconds. Express this time in minutes as a dec…
30 seconds is half of a minute, so 30 seconds = 0.5 minutes. Add this to the 7 minutes: 7 + 0.5 = 7.5 minutes.
A fire sprinkler system covers 1500 square feet. If 1/5 of the system needs maintenance, how many square fe…
Multiply the total area by the fraction: (1/5) * 1500 square feet = 300 square feet.
A room measures 10 meters by 8 meters. What is its area in square meters?
To find the area of a rectangle, multiply length by width: 10 meters * 8 meters = 80 square meters.
What is the result of 1/2 + 1/4?
To add fractions, find a common denominator. 1/2 can be written as 2/4. Then add: 2/4 + 1/4 = 3/4.
A ladder truck has a total weight capacity of 7,000 kg. If the truck itself weighs 5,500 kg, and there are …
Calculate the total weight of the truck and firefighters: 5,500 kg + (4 firefighters * 90 kg/firefighter) = 5,500 kg + 360 kg = 5,860 kg. Then, subtract this fr
A fire department's budget for training is $15,000. If 40% of the budget is allocated to new equipment, how…
First, calculate the amount allocated to new equipment: $15,000 * 0.40 = $6,000. Then, subtract this from the total budget: $15,000 - $6,000 = $9,000.
A building has 5 floors. Each floor is 12 feet high. What is the total height of the building in feet?
Multiply the number of floors by the height of each floor: 5 floors * 12 feet/floor = 60 feet.
A fire crew works a 24-hour shift. If they have a 45-minute break for lunch and a 30-minute break for dinne…
Total break time = 45 minutes + 30 minutes = 75 minutes. Convert 75 minutes to hours and minutes: 1 hour and 15 minutes. Subtract total break time from total sh
A hose line has a flow rate of 150 GPM. If it needs to fill a portable tank with a capacity of 1,200 gallon…
Divide the tank capacity by the flow rate: 1,200 gallons / 150 GPM = 8 minutes.
Convert 2.5 meters to centimeters.
There are 100 centimeters in 1 meter. So, 2.5 meters * 100 cm/meter = 250 cm.
A pump delivers 1,000 GPM. If it runs for 1.5 hours, how many gallons of water are delivered?
First, convert 1.5 hours to minutes: 1.5 hours * 60 minutes/hour = 90 minutes. Then, multiply the flow rate by the time in minutes: 1,000 GPM * 90 minutes = 90,
Which of the following decimals is equivalent to 1/8?
To convert a fraction to a decimal, divide the numerator by the denominator: 1 / 8 = 0.125.
A structure fire requires two hose lines flowing at 150 GPM each. A third master stream device flows at 500…
Calculate the flow from two hose lines: 2 * 150 GPM = 300 GPM. Then, add the master stream flow: 300 GPM + 500 GPM = 800 GPM.
The diameter of a hose is 65 mm. What is this measurement in inches, approximately? (1 inch = 2.54 cm)
First, convert mm to cm: 65 mm = 6.5 cm. Then, convert cm to inches: 6.5 cm / 2.54 cm/inch ≈ 2.56 inches.
A search team is tasked to search an area of 400 square meters. If they have covered 0.6 of the area, how m…
If 0.6 of the area is covered, then 1 - 0.6 = 0.4 of the area is left. Multiply the total area by this decimal: 0.4 * 400 square meters = 160 square meters.
An air cylinder provides 45 minutes of air. If a firefighter uses 2/3 of the air, how many minutes of air a…
If 2/3 of the air is used, then 1 - 2/3 = 1/3 of the air is remaining. Calculate 1/3 of the total air time: (1/3) * 45 minutes = 15 minutes.
A three-person crew can complete a task in 6 hours. If the task requires a total of 18 person-hours, how lo…
The total work is 18 person-hours. For a two-person crew, divide the total work by the number of people: 18 person-hours / 2 people = 9 hours.
What is the equivalent fraction for 0.75?
0.75 can be written as 75/100. This fraction can be simplified by dividing both numerator and denominator by 25, resulting in 3/4.
If the specific gravity of a liquid is 0.9, and water has a specific gravity of 1.0, what does this imply a…
Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). A specific gravity less than 1.0 means the
A team of 5 firefighters responds to an incident. If 20% of the team is assigned to ventilation, how many f…
To find 20% of 5, convert the percentage to a decimal (0.20) and multiply: 0.20 * 5 = 1 firefighter.
A fire hose has a friction loss of 15 PSI per 100 feet. If a hose lay is 400 feet, what is the total fricti…
Since the friction loss is 15 PSI per 100 feet, for a 400-foot hose, the loss is (400 feet / 100 feet) * 15 PSI = 4 * 15 PSI = 60 PSI.
How many days are in 3.5 weeks?
Multiply the number of weeks by 7 (days in a week): 3.5 weeks * 7 days/week = 24.5 days.
A municipal fire department has a fleet of 20 vehicles. If 1/4 of them are reserve units, how many active u…
If 1/4 are reserve units, then 1 - 1/4 = 3/4 are active units. Calculate 3/4 of the total fleet: (3/4) * 20 = 15 active units.
The elevation from the pump to the nozzle is 20 feet. If 1 PSI lifts water approximately 2.3 feet, what is …
Divide the elevation by the conversion factor for head pressure: 20 feet / 2.3 feet/PSI ≈ 8.695 PSI, which rounds to 8.7 PSI. (For exam purposes, round accordin
If a pumper is rated to discharge 1000 GPM, and it's operating at 80% capacity, what is its actual discharg…
Multiply the rated capacity by the operating percentage: 1000 GPM * 0.80 = 800 GPM.
A self-contained breathing apparatus (SCBA) cylinder holds 4500 PSI. If a firefighter starts a task with 3/…
Calculate 3/4 of the total pressure: (3/4) * 4500 PSI = 3375 PSI.
If pump discharge pressure (PDP) is 180 PSI and nozzle pressure (NP) is 100 PSI, what is the total friction…
Total pressure loss between the pump and nozzle is PDP - NP. So, 180 PSI - 100 PSI = 80 PSI.
A fire station has 3 shifts. Each shift has 1 captain, 1 rescue officer, and 3 firefighters. How many perso…
First, calculate the personnel per shift: 1 (captain) + 1 (rescue officer) + 3 (firefighters) = 5 personnel. Then, multiply by the number of shifts: 5 personnel
A water tender carries 2,000 gallons. If it makes 3 trips to the scene, how many gallons of water are deliv…
Multiply the capacity per trip by the number of trips: 2,000 gallons/trip * 3 trips = 6,000 gallons.
An emergency response vehicle travels 120 km in 1 hour and 30 minutes. What is its speed in km/h?
Convert 1 hour and 30 minutes to hours: 1 + 30/60 = 1.5 hours. Then, divide distance by time: 120 km / 1.5 hours = 80 km/h.
If a nozzle is flowing at 250 GPM and the pump pressure is 150 PSI, what is the approximate friction loss p…
If two 100-foot sections have a friction loss of 80 PSI, then one 100-foot section would have half that, which is 80 PSI / 2 = 40 PSI.
What is the sum of five and three-quarters?
Three-quarters as a decimal is 0.75. Add this to five: 5 + 0.75 = 5.75.
A fire truck's fuel tank is 3/5 full. If it holds 100 litres when full, how many litres of fuel are in the …
Multiply the total capacity by the fraction: (3/5) * 100 litres = 60 litres.
A hazmat team is dealing with a spill of 250 litres. If they successfully contain 90% of the spill, how man…
Calculate 90% of the total spill volume: 250 litres * 0.90 = 225 litres.
A fire department has 12 engines and 4 ladder trucks. What is the ratio of engines to ladder trucks?
The ratio of engines to ladder trucks is 12:4. This can be simplified by dividing both numbers by their greatest common divisor (4): 12/4 : 4/4 = 3:1.
Scenario 1: A fire engine carries 500 gallons of water. If the pump is flowing at 125 gallons per minute (G…
To find out how long the water will last, divide the total water volume by the flow rate: 500 gallons / 125 GPM = 4 minutes. The correct answer is "4 minutes".
Scenario 64: A fire engine carries 500 gallons of water. If the pump is flowing at 125 gallons per minute (…
To find out how long the water will last, divide the total water volume by the flow rate: 500 gallons / 125 GPM = 4 minutes. The correct answer is "4 minutes".
Scenario 2: What is 3/4 of 120?
To find 3/4 of 120, multiply 120 by 3/4: (3/4) * 120 = 90. The correct answer is "90". This reflects the accepted standard for the firefighter-math assessment a
A fire station receives 18 calls in a 24-hour period. What is the average number of calls per hour?
Divide the total number of calls by the total hours: 18 calls / 24 hours = 0.75 calls per hour.
Scenario 65: What is 3/4 of 120?
To find 3/4 of 120, multiply 120 by 3/4: (3/4) * 120 = 90. The correct answer is "90". This reflects the accepted standard for the firefighter-math assessment a
Scenario 3: A fire truck travels 60 km in 45 minutes. What is its average speed in km/h?
First, convert 45 minutes to hours: 45 minutes / 60 minutes/hour = 0.75 hours. Then, divide distance by time to get speed: 60 km / 0.75 hours = 80 km/h. The cor
Scenario 66: A fire truck travels 60 km in 45 minutes. What is its average speed in km/h?
First, convert 45 minutes to hours: 45 minutes / 60 minutes/hour = 0.75 hours. Then, divide distance by time to get speed: 60 km / 0.75 hours = 80 km/h. The cor
Scenario 4: A hose line has a flow rate of 150 GPM. If it needs to fill a portable tank with a capacity of …
Divide the tank capacity by the flow rate: 1,200 gallons / 150 GPM = 8 minutes. The correct answer is "8 minutes". This capacity-fill scenario 4 reinforces the
Scenario 67: A hose line has a flow rate of 150 GPM. If it needs to fill a portable tank with a capacity of…
Divide the tank capacity by the flow rate: 1,200 gallons / 150 GPM = 8 minutes. The correct answer is "8 minutes". This capacity-fill scenario 67 reinforces the
Scenario 5: Convert 2.5 meters to centimeters.
There are 100 centimeters in 1 meter. So, 2.5 meters * 100 cm/meter = 250 cm. The correct answer is "250 cm". This capacity-fill scenario 5 reinforces the same
Scenario 68: Convert 2.5 meters to centimeters.
There are 100 centimeters in 1 meter. So, 2.5 meters * 100 cm/meter = 250 cm. The correct answer is "250 cm". This capacity-fill scenario 68 reinforces the same
Scenario 6: A fire department has 12 engines and 4 ladder trucks. What is the ratio of engines to ladder tr…
The ratio of engines to ladder trucks is 12:4. This can be simplified by dividing both numbers by their greatest common divisor (4): 12/4 : 4/4 = 3:1. The corre
Scenario 69: A fire department has 12 engines and 4 ladder trucks. What is the ratio of engines to ladder t…
The ratio of engines to ladder trucks is 12:4. This can be simplified by dividing both numbers by their greatest common divisor (4): 12/4 : 4/4 = 3:1. The corre
Scenario 7: During a wildfire, firefighters consumed 750 litres of water from a 1000-litre tank. What perce…
Divide the amount of water used by the total capacity, then multiply by 100 to get the percentage: (750 litres / 1000 litres) * 100% = 75%. The correct answer i
Scenario 70: During a wildfire, firefighters consumed 750 litres of water from a 1000-litre tank. What perc…
Divide the amount of water used by the total capacity, then multiply by 100 to get the percentage: (750 litres / 1000 litres) * 100% = 75%. The correct answer i
Scenario 8: A pump delivers 1,000 GPM. If it runs for 1.5 hours, how many gallons of water are delivered?
First, convert 1.5 hours to minutes: 1.5 hours * 60 minutes/hour = 90 minutes. Then, multiply the flow rate by the time in minutes: 1,000 GPM * 90 minutes = 90,
Scenario 71: A pump delivers 1,000 GPM. If it runs for 1.5 hours, how many gallons of water are delivered?
First, convert 1.5 hours to minutes: 1.5 hours * 60 minutes/hour = 90 minutes. Then, multiply the flow rate by the time in minutes: 1,000 GPM * 90 minutes = 90,
Scenario 9: Which of the following decimals is equivalent to 1/8?
To convert a fraction to a decimal, divide the numerator by the denominator: 1 / 8 = 0.125. The correct answer is "0.125". This capacity-fill scenario 9 reinfor
Scenario 72: Which of the following decimals is equivalent to 1/8?
To convert a fraction to a decimal, divide the numerator by the denominator: 1 / 8 = 0.125. The correct answer is "0.125". This capacity-fill scenario 72 reinfo
Scenario 10: A structure fire requires two hose lines flowing at 150 GPM each. A third master stream device…
Calculate the flow from two hose lines: 2 * 150 GPM = 300 GPM. Then, add the master stream flow: 300 GPM + 500 GPM = 800 GPM. The correct answer is "800 GPM". T
Scenario 73: A structure fire requires two hose lines flowing at 150 GPM each. A third master stream device…
Calculate the flow from two hose lines: 2 * 150 GPM = 300 GPM. Then, add the master stream flow: 300 GPM + 500 GPM = 800 GPM. The correct answer is "800 GPM". T
Scenario 11: The diameter of a hose is 65 mm. What is this measurement in inches, approximately? (1 inch = …
First, convert mm to cm: 65 mm = 6.5 cm. Then, convert cm to inches: 6.5 cm / 2.54 cm/inch ≈ 2.56 inches. The correct answer is "2.56 inches". This capacity-fil
Scenario 74: The diameter of a hose is 65 mm. What is this measurement in inches, approximately? (1 inch = …
First, convert mm to cm: 65 mm = 6.5 cm. Then, convert cm to inches: 6.5 cm / 2.54 cm/inch ≈ 2.56 inches. The correct answer is "2.56 inches". This capacity-fil
Scenario 12: A fire hose is 300 feet long. If 1/3 of the hose is deployed, how many feet of hose remain on …
If 1/3 of the hose is deployed, then 2/3 of the hose remains. (2/3) * 300 feet = 200 feet. The correct answer is "200 feet". This capacity-fill scenario 12 rein
Scenario 75: A fire hose is 300 feet long. If 1/3 of the hose is deployed, how many feet of hose remain on …
If 1/3 of the hose is deployed, then 2/3 of the hose remains. (2/3) * 300 feet = 200 feet. The correct answer is "200 feet". This capacity-fill scenario 75 rein
Scenario 13: A fire truck's fuel tank is 3/5 full. If it holds 100 litres when full, how many litres of fue…
Multiply the total capacity by the fraction: (3/5) * 100 litres = 60 litres. The correct answer is "60 litres". This capacity-fill scenario 13 reinforces the sa
Scenario 76: A fire truck's fuel tank is 3/5 full. If it holds 100 litres when full, how many litres of fue…
Multiply the total capacity by the fraction: (3/5) * 100 litres = 60 litres. The correct answer is "60 litres". This capacity-fill scenario 76 reinforces the sa
Scenario 14: What is 15% of 300?
To find 15% of 300, convert the percentage to a decimal (0.15) and multiply: 0.15 * 300 = 45. The correct answer is "45". This capacity-fill scenario 14 reinfor
Scenario 77: What is 15% of 300?
To find 15% of 300, convert the percentage to a decimal (0.15) and multiply: 0.15 * 300 = 45. The correct answer is "45". This capacity-fill scenario 77 reinfor
Scenario 15: A fire department's budget increased from $1,200,000 to $1,260,000. What is the percentage inc…
Calculate the increase: $1,260,000 - $1,200,000 = $60,000. Divide the increase by the original budget and multiply by 100: ($60,000 / $1,200,000) * 100% = 5%. T
Scenario 78: A fire department's budget increased from $1,200,000 to $1,260,000. What is the percentage inc…
Calculate the increase: $1,260,000 - $1,200,000 = $60,000. Divide the increase by the original budget and multiply by 100: ($60,000 / $1,200,000) * 100% = 5%. T
Scenario 16: If 1 Canadian gallon is approximately 4.54 litres, how many litres are in a 500-gallon water t…
Multiply the tank capacity in gallons by the conversion factor: 500 gallons * 4.54 litres/gallon = 2270 litres. The correct answer is "2270 litres". This capaci
Scenario 79: If 1 Canadian gallon is approximately 4.54 litres, how many litres are in a 500-gallon water t…
Multiply the tank capacity in gallons by the conversion factor: 500 gallons * 4.54 litres/gallon = 2270 litres. The correct answer is "2270 litres". This capaci
Scenario 17: A search team is tasked to search an area of 400 square meters. If they have covered 0.6 of th…
If 0.6 of the area is covered, then 1 - 0.6 = 0.4 of the area is left. Multiply the total area by this decimal: 0.4 * 400 square meters = 160 square meters. The
Scenario 80: A search team is tasked to search an area of 400 square meters. If they have covered 0.6 of th…
If 0.6 of the area is covered, then 1 - 0.6 = 0.4 of the area is left. Multiply the total area by this decimal: 0.4 * 400 square meters = 160 square meters. The
Scenario 18: An air cylinder provides 45 minutes of air. If a firefighter uses 2/3 of the air, how many min…
If 2/3 of the air is used, then 1 - 2/3 = 1/3 of the air is remaining. Calculate 1/3 of the total air time: (1/3) * 45 minutes = 15 minutes. The correct answer
Scenario 81: An air cylinder provides 45 minutes of air. If a firefighter uses 2/3 of the air, how many min…
If 2/3 of the air is used, then 1 - 2/3 = 1/3 of the air is remaining. Calculate 1/3 of the total air time: (1/3) * 45 minutes = 15 minutes. The correct answer
Scenario 19: A three-person crew can complete a task in 6 hours. If the task requires a total of 18 person-…
The total work is 18 person-hours. For a two-person crew, divide the total work by the number of people: 18 person-hours / 2 people = 9 hours. The correct answe
Scenario 82: A three-person crew can complete a task in 6 hours. If the task requires a total of 18 person-…
The total work is 18 person-hours. For a two-person crew, divide the total work by the number of people: 18 person-hours / 2 people = 9 hours. The correct answe
Scenario 20: What is the equivalent fraction for 0.75?
0.75 can be written as 75/100. This fraction can be simplified by dividing both numerator and denominator by 25, resulting in 3/4. The correct answer is "3/4".
Scenario 83: What is the equivalent fraction for 0.75?
0.75 can be written as 75/100. This fraction can be simplified by dividing both numerator and denominator by 25, resulting in 3/4. The correct answer is "3/4".
Scenario 21: A hydrant provides water at a rate of 1,000 litres per minute. How many litres will it provide…
Multiply the flow rate by the time: 1,000 litres/minute * 15 minutes = 15,000 litres. The correct answer is "15,000 litres". This capacity-fill scenario 21 rein
Scenario 84: A hydrant provides water at a rate of 1,000 litres per minute. How many litres will it provide…
Multiply the flow rate by the time: 1,000 litres/minute * 15 minutes = 15,000 litres. The correct answer is "15,000 litres". This capacity-fill scenario 84 rein
Scenario 22: A room measures 10 meters by 8 meters. What is its area in square meters?
To find the area of a rectangle, multiply length by width: 10 meters * 8 meters = 80 square meters. The correct answer is "80 square meters". This capacity-fill
Scenario 85: A room measures 10 meters by 8 meters. What is its area in square meters?
To find the area of a rectangle, multiply length by width: 10 meters * 8 meters = 80 square meters. The correct answer is "80 square meters". This capacity-fill
Scenario 23: A firefighter earns an annual salary of $60,000. If they receive a 2.5% raise, what is their n…
First, calculate the raise amount: $60,000 * 0.025 = $1,500. Then, add the raise to the original salary: $60,000 + $1,500 = $61,500. The correct answer is "$61,
Scenario 86: A firefighter earns an annual salary of $60,000. If they receive a 2.5% raise, what is their n…
First, calculate the raise amount: $60,000 * 0.025 = $1,500. Then, add the raise to the original salary: $60,000 + $1,500 = $61,500. The correct answer is "$61,
Scenario 24: If the specific gravity of a liquid is 0.9, and water has a specific gravity of 1.0, what does…
Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). A specific gravity less than 1.0 means the
Scenario 87: If the specific gravity of a liquid is 0.9, and water has a specific gravity of 1.0, what does…
Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). A specific gravity less than 1.0 means the
Scenario 25: A team of 5 firefighters responds to an incident. If 20% of the team is assigned to ventilatio…
To find 20% of 5, convert the percentage to a decimal (0.20) and multiply: 0.20 * 5 = 1 firefighter. The correct answer is "1 firefighter". This capacity-fill s
Scenario 26: A fire hose has a friction loss of 15 PSI per 100 feet. If a hose lay is 400 feet, what is the…
Since the friction loss is 15 PSI per 100 feet, for a 400-foot hose, the loss is (400 feet / 100 feet) * 15 PSI = 4 * 15 PSI = 60 PSI. The correct answer is "60
Scenario 27: How many days are in 3.5 weeks?
Multiply the number of weeks by 7 (days in a week): 3.5 weeks * 7 days/week = 24.5 days. The correct answer is "24.5 days". This capacity-fill scenario 27 reinf
Scenario 28: A municipal fire department has a fleet of 20 vehicles. If 1/4 of them are reserve units, how …
If 1/4 are reserve units, then 1 - 1/4 = 3/4 are active units. Calculate 3/4 of the total fleet: (3/4) * 20 = 15 active units. The correct answer is "15 units".
Scenario 29: The elevation from the pump to the nozzle is 20 feet. If 1 PSI lifts water approximately 2.3 f…
Divide the elevation by the conversion factor for head pressure: 20 feet / 2.3 feet/PSI ≈ 8.695 PSI, which rounds to 8.7 PSI. (For exam purposes, round accordin
Scenario 30: A firefighter spent $45 on new gloves and $25 on a new helmet light. What was the total cost?
Add the two costs together: $45 + $25 = $70. The correct answer is "$70". This reflects the accepted standard for the firefighter-math assessment and aligns wit
Scenario 31: If a pumper is rated to discharge 1000 GPM, and it's operating at 80% capacity, what is its ac…
Multiply the rated capacity by the operating percentage: 1000 GPM * 0.80 = 800 GPM. The correct answer is "800 GPM". This capacity-fill scenario 31 reinforces t
Scenario 32: What is the result of 1/2 + 1/4?
To add fractions, find a common denominator. 1/2 can be written as 2/4. Then add: 2/4 + 1/4 = 3/4. The correct answer is "3/4". This capacity-fill scenario 32 r
Scenario 33: A wildfire is spreading at a rate of 1.5 acres per hour. How many acres will it cover in 6 hours?
Multiply the spread rate by the time: 1.5 acres/hour * 6 hours = 9 acres. The correct answer is "9 acres". This capacity-fill scenario 33 reinforces the same co
Scenario 34: A ladder truck has a total weight capacity of 7,000 kg. If the truck itself weighs 5,500 kg, a…
Calculate the total weight of the truck and firefighters: 5,500 kg + (4 firefighters * 90 kg/firefighter) = 5,500 kg + 360 kg = 5,860 kg. Then, subtract this fr
Scenario 35: A self-contained breathing apparatus (SCBA) cylinder holds 4500 PSI. If a firefighter starts a…
Calculate 3/4 of the total pressure: (3/4) * 4500 PSI = 3375 PSI. The correct answer is "3375 PSI". This capacity-fill scenario 35 reinforces the same competenc
Scenario 36: A fire truck uses 50 litres of fuel for every 100 km driven. How many litres will it use to dr…
Set up a proportion: (50 litres / 100 km) = (x litres / 250 km). Solve for x: x = (50 * 250) / 100 = 125 litres. The correct answer is "125 litres". This capaci
Scenario 37: The average response time to an incident is 7 minutes and 30 seconds. Express this time in min…
30 seconds is half of a minute, so 30 seconds = 0.5 minutes. Add this to the 7 minutes: 7 + 0.5 = 7.5 minutes. The correct answer is "7.5 minutes". This capacit
Scenario 38: A fire sprinkler system covers 1500 square feet. If 1/5 of the system needs maintenance, how m…
Multiply the total area by the fraction: (1/5) * 1500 square feet = 300 square feet. The correct answer is "300 square feet". This capacity-fill scenario 38 rei
Scenario 39: The total length of hose needed for an operation is 600 feet. If hoses are available in 150-fo…
Divide the total length needed by the length of each section: 600 feet / 150 feet/section = 4 sections. The correct answer is "4 sections". This capacity-fill s
Scenario 40: A hazmat team is dealing with a spill of 250 litres. If they successfully contain 90% of the s…
Calculate 90% of the total spill volume: 250 litres * 0.90 = 225 litres. The correct answer is "225 litres". This capacity-fill scenario 40 reinforces the same
Scenario 41: If pump discharge pressure (PDP) is 180 PSI and nozzle pressure (NP) is 100 PSI, what is the t…
Total pressure loss between the pump and nozzle is PDP - NP. So, 180 PSI - 100 PSI = 80 PSI. The correct answer is "80 PSI". This capacity-fill scenario 41 rein
Scenario 42: A fire station has 3 shifts. Each shift has 1 captain, 1 rescue officer, and 3 firefighters. H…
First, calculate the personnel per shift: 1 (captain) + 1 (rescue officer) + 3 (firefighters) = 5 personnel. Then, multiply by the number of shifts: 5 personnel
Scenario 43: What is the sum of five and three-quarters?
Three-quarters as a decimal is 0.75. Add this to five: 5 + 0.75 = 5.75. The correct answer is "5.75". This capacity-fill scenario 43 reinforces the same compete
Scenario 44: A water tender carries 2,000 gallons. If it makes 3 trips to the scene, how many gallons of wa…
Multiply the capacity per trip by the number of trips: 2,000 gallons/trip * 3 trips = 6,000 gallons. The correct answer is "6,000 gallons". This capacity-fill s
Scenario 45: A fire station receives 18 calls in a 24-hour period. What is the average number of calls per …
Divide the total number of calls by the total hours: 18 calls / 24 hours = 0.75 calls per hour. The correct answer is "0.75 calls/hour". This capacity-fill scen
Scenario 46: An emergency response vehicle travels 120 km in 1 hour and 30 minutes. What is its speed in km/h?
Convert 1 hour and 30 minutes to hours: 1 + 30/60 = 1.5 hours. Then, divide distance by time: 120 km / 1.5 hours = 80 km/h. The correct answer is "80 km/h". Thi
Scenario 47: A fire department has 8 engines, 3 ladder trucks, and 2 rescue units. What fraction of the tot…
First, find the total number of apparatus: 8 + 3 + 2 = 13. Then, form the fraction of ladder trucks to total: 3/13. The correct answer is "3/13". This capacity-
Scenario 48: If a nozzle is flowing at 250 GPM and the pump pressure is 150 PSI, what is the approximate fr…
If two 100-foot sections have a friction loss of 80 PSI, then one 100-foot section would have half that, which is 80 PSI / 2 = 40 PSI. The correct answer is "40
Scenario 49: A fire department's budget for training is $15,000. If 40% of the budget is allocated to new e…
First, calculate the amount allocated to new equipment: $15,000 * 0.40 = $6,000. Then, subtract this from the total budget: $15,000 - $6,000 = $9,000. The corre
Scenario 50: A building has 5 floors. Each floor is 12 feet high. What is the total height of the building …
Multiply the number of floors by the height of each floor: 5 floors * 12 feet/floor = 60 feet. The correct answer is "60 feet". This capacity-fill scenario 50 r
Scenario 51: A fire crew works a 24-hour shift. If they have a 45-minute break for lunch and a 30-minute br…
Total break time = 45 minutes + 30 minutes = 75 minutes. Convert 75 minutes to hours and minutes: 1 hour and 15 minutes. Subtract total break time from total sh
Scenario 52: Solve for x: 3x − 7 = 14
3x = 21 → x = 7. The correct answer is "7". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for th
Scenario 53: Convert 3/4 to a decimal:
3 ÷ 4 = 0.75. The correct answer is "0.75". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for th
Scenario 54: What is 20% of 350?
0.20 × 350 = 70. The correct answer is "70". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for t
Scenario 55: A truck carries 1,000 gallons. It used 350 gal at one fire and 275 at another. Gallons remaining:
1000 − 350 − 275 = 375. The correct answer is "375". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbo
Scenario 56: Convert 5 km to meters:
1 km = 1,000 m; 5 × 1,000 = 5,000 m. The correct answer is "5,000 m". This reflects the accepted standard for the firefighter-math assessment and aligns with th
Scenario 57: Area of a rectangular room 12 ft × 15 ft:
Area = L × W = 12 × 15 = 180 sq ft. The correct answer is "180 sq ft". This reflects the accepted standard for the firefighter-math assessment and aligns with t
Scenario 58: A hose flows at 150 GPM for 4 minutes. Total water delivered:
150 × 4 = 600 gallons. The correct answer is "600 gal". This reflects the accepted standard for the firefighter-math assessment and aligns with the official han
Scenario 59: Friction loss formula commonly used: FL = C × Q^2 × L. For a 1¾'' line (C=15.5), Q=1.5 (150 GP…
FL = 15.5 × 1.5^2 × 2 = 15.5 × 2.25 × 2 = 69.75 ≈ 70 psi. The correct answer is "~70 psi". This reflects the accepted standard for the firefighter-math assessme
Scenario 60: Pump discharge pressure (PDP) = Nozzle Pressure + Friction Loss + Elevation. NP=100 psi, FL=30…
Elevation = 20 × 0.5 = 10 psi. PDP = 100 + 30 + 10 = 140 psi. The correct answer is "140 psi". This capacity-fill scenario 60 reinforces the same competency for
Scenario 61: Pump flows 250 GPM. To deliver 5,000 gallons takes:
5000 ÷ 250 = 20 minutes. The correct answer is "20 min". This reflects the accepted standard for the firefighter-math assessment and aligns with the official ha
Scenario 62: To mix a 3% foam solution in 200 gallons of water, how much foam concentrate is needed?
3% × 200 = 6 gallons of foam concentrate. The correct answer is "6 gal". This reflects the accepted standard for the firefighter-math assessment and aligns with
Scenario 63: A cylindrical tank radius 2 m, height 3 m. Volume (π≈3.14):
V = π r² h = 3.14 × 4 × 3 ≈ 37.7 m³. The correct answer is "~37.7 m³". This reflects the accepted standard for the firefighter-math assessment and aligns with t
Solve for x: 3x − 7 = 14
3x = 21 → x = 7. The correct answer is "7". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for th
Convert 3/4 to a decimal:
3 ÷ 4 = 0.75. The correct answer is "0.75". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for th
What is 20% of 350?
0.20 × 350 = 70. The correct answer is "70". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbook for t
Pump discharge pressure (PDP) = Nozzle Pressure + Friction Loss + Elevation. NP=100 psi, FL=30 psi, Elevati…
Elevation = 20 × 0.5 = 10 psi. PDP = 100 + 30 + 10 = 140 psi.
A truck carries 1,000 gallons. It used 350 gal at one fire and 275 at another. Gallons remaining:
1000 − 350 − 275 = 375. The correct answer is "375". This reflects the accepted standard for the firefighter-math assessment and aligns with the official handbo
Convert 5 km to meters:
1 km = 1,000 m; 5 × 1,000 = 5,000 m. The correct answer is "5,000 m". This reflects the accepted standard for the firefighter-math assessment and aligns with th
If 1 Canadian gallon is approximately 4.54 litres, how many litres are in a 500-gallon water tank?
Multiply the tank capacity in gallons by the conversion factor: 500 gallons * 4.54 litres/gallon = 2270 litres.
A fire department's budget increased from $1,200,000 to $1,260,000. What is the percentage increase?
Calculate the increase: $1,260,000 - $1,200,000 = $60,000. Divide the increase by the original budget and multiply by 100: ($60,000 / $1,200,000) * 100% = 5%.
During a wildfire, firefighters consumed 750 litres of water from a 1000-litre tank. What percentage of the…
Divide the amount of water used by the total capacity, then multiply by 100 to get the percentage: (750 litres / 1000 litres) * 100% = 75%.
A wildfire is spreading at a rate of 1.5 acres per hour. How many acres will it cover in 6 hours?
Multiply the spread rate by the time: 1.5 acres/hour * 6 hours = 9 acres.
The total length of hose needed for an operation is 600 feet. If hoses are available in 150-foot sections, …
Divide the total length needed by the length of each section: 600 feet / 150 feet/section = 4 sections.
A fire truck travels 60 km in 45 minutes. What is its average speed in km/h?
First, convert 45 minutes to hours: 45 minutes / 60 minutes/hour = 0.75 hours. Then, divide distance by time to get speed: 60 km / 0.75 hours = 80 km/h.
A fire truck uses 50 litres of fuel for every 100 km driven. How many litres will it use to drive 250 km?
Set up a proportion: (50 litres / 100 km) = (x litres / 250 km). Solve for x: x = (50 * 250) / 100 = 125 litres.
A firefighter earns an annual salary of $60,000. If they receive a 2.5% raise, what is their new annual sal…
First, calculate the raise amount: $60,000 * 0.025 = $1,500. Then, add the raise to the original salary: $60,000 + $1,500 = $61,500.
A fire engine carries 500 gallons of water. If the pump is flowing at 125 gallons per minute (GPM), how lon…
To find out how long the water will last, divide the total water volume by the flow rate: 500 gallons / 125 GPM = 4 minutes.
A fire hose is 300 feet long. If 1/3 of the hose is deployed, how many feet of hose remain on the truck?
If 1/3 of the hose is deployed, then 2/3 of the hose remains. (2/3) * 300 feet = 200 feet.
A fire department has 8 engines, 3 ladder trucks, and 2 rescue units. What fraction of the total apparatus …
First, find the total number of apparatus: 8 + 3 + 2 = 13. Then, form the fraction of ladder trucks to total: 3/13.
A hydrant provides water at a rate of 1,000 litres per minute. How many litres will it provide in 15 minutes?
Multiply the flow rate by the time: 1,000 litres/minute * 15 minutes = 15,000 litres.
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