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Mathematical Reasoning Flashcards

6 cards from real CPS practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Mathematical Reasoning flashcards as text

  1. A fire engine's water tank holds 500 gallons. If the crew is attacking a fire with a hoseline flowing at 125 gallons per minute (GPM), how many minutes will the tank's water supply last?

    Answer: 4 minutes

    To determine how long the water supply will last, divide the total volume of water in the tank by the flow rate of the hoseline. 500 gallons / 125 GPM = 4 minutes.

  2. A firefighter must carry two 50-foot sections of 1.75-inch hose up three flights of stairs. If each 50-foot section weighs 28 pounds when empty, what is the total weight of the hose the firefighter is carrying?

    Answer: 56 pounds

    The question asks for the total weight of the two sections of hose being carried. Multiply the weight of one section by the number of sections: 28 pounds/section * 2 sections = 56 pounds. The number of stairs is extra information not needed for the calculation.

  3. A fire has occurred in a rectangular room that measures 50 feet long by 30 feet wide. What is the total square footage of the room?

    Answer: 1,500 square feet

    To find the area of a rectangle, you multiply its length by its width. In this case, 50 feet * 30 feet = 1,500 square feet.

  4. An engine company is dispatched to a call 9 miles away. If the engine travels at an average speed of 36 miles per hour, how many minutes will it take to arrive at the scene?

    Answer: 15 minutes

    First, calculate the travel time in hours by dividing the distance by the speed (Time = Distance / Speed). So, 9 miles / 36 mph = 0.25 hours. To convert hours to minutes, multiply by 60: 0.25 * 60 = 15 minutes.

  5. A firefighter needs to use a 3% foam concentrate to extinguish a flammable liquid fire. If the total amount of foam solution needed is 150 gallons, how many gallons of foam concentrate are required?

    Answer: 4.5 gallons

    To calculate the amount of foam concentrate, convert the percentage to a decimal (3% = 0.03) and multiply it by the total solution volume. 150 gallons * 0.03 = 4.5 gallons.

  6. A ladder must be raised to a window that is 24 feet above the ground. To be placed at the proper angle, the base of the ladder should be 7 feet away from the building. What is the minimum length the ladder must be to reach the window?

    Answer: 25 feet

    This problem forms a right triangle and can be solved using the Pythagorean theorem (a² + b² = c²). The height (24 feet) and the distance from the building (7 feet) are the legs. So, 24² + 7² = c². This becomes 576 + 49 = c², which equals 625. The square root of 625 is 25. Therefore, the ladder must be at least 25 feet long.