Praxis Math Quiz: Apply Constant Rates
20 questions · exam conditions
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Apply Constant RatesQuestion 1 of 20

A tank is filled by an inlet pipe at a constant rate of 12 gallons per minute. At the same time, water is drained from the tank by an outlet pipe at a constant rate of 4 gallons per minute. If the tank is empty and has a capacity of 300 gallons, how long will it take to fill the tank completely?

18.75 minutes
25.0 minutes
37.5 minutes
75.0 minutes
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Praxis Math Quiz

Praxis Math Quiz: Apply Constant Rates

Practice Apply Constant Rates in Praxis Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Apply Constant Rates, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

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Question 1

A tank is filled by an inlet pipe at a constant rate of 12 gallons per minute. At the same time, water is drained from the tank by an outlet pipe at a constant rate of 4 gallons per minute. If the tank is empty and has a capacity of 300 gallons, how long will it take to fill the tank completely?

  1. 18.75 minutes
  2. 25.0 minutes
  3. 37.5 minutes (correct answer)
  4. 75.0 minutes
Explanation: First, find the net filling rate. Since water is entering and leaving simultaneously, subtract the outlet rate from the inlet rate. Net rate = 12 gallons/minute - 4 gallons/minute = 8 gallons/minute. Now, use this net rate to find the time to fill the 300-gallon tank. Time = Total Volume / Net Rate. Time = 300 gallons / 8 gallons/minute = 37.5 minutes.

Question 2

Two cyclists start at the same point and travel in opposite directions along a straight road. Cyclist A travels at a constant speed of 14 miles per hour, and Cyclist B travels at a constant speed of 18 miles per hour. How much time will have passed when they are 88 miles apart?

  1. 2.20 hours
  2. 2.75 hours (correct answer)
  3. 6.28 hours
  4. 22.00 hours
Explanation: When two objects move in opposite directions, their relative speed is the sum of their individual speeds. The rate at which the distance between them is increasing is 14 mph + 18 mph = 32 mph. To find the time it takes for them to be 88 miles apart, use the formula Time = Distance / Rate. Time = 88 miles / 32 mph = 2.75 hours.

Question 3

Jamal starts driving from his house at a constant speed of 40 mph. His sister, Kira, leaves the same house 30 minutes later, driving along the same route at a constant speed of 50 mph. How long will it take Kira to catch up to Jamal?

  1. 1.5 hours
  2. 2.0 hours (correct answer)
  3. 2.5 hours
  4. 3.0 hours
Explanation: First, determine how far Jamal has traveled in the 30 minutes (0.5 hours) before Kira starts. Distance = Speed × Time = 40 mph × 0.5 hours = 20 miles. This is Jamal's head start. Kira gains on Jamal at a rate equal to the difference in their speeds: 50 mph - 40 mph = 10 mph. To find the time it takes for Kira to cover the 20-mile gap, use Time = Distance / Rate. Time = 20 miles / 10 mph = 2.0 hours.

Question 4

Three identical machines can produce a total of 540 parts in 6 hours. If two of the machines break down, how long will it take the remaining machine to produce 270 parts, assuming it works at the same constant rate?

  1. 9 hours (correct answer)
  2. 12 hours
  3. 15 hours
  4. 18 hours
Explanation: First, find the production rate for the group of three machines: 540 parts / 6 hours = 90 parts/hour. Since the three machines are identical, the rate of a single machine is 90 parts/hour / 3 machines = 30 parts/hour. To find the time for one machine to produce 270 parts, divide the total parts by the single machine's rate: Time = 270 parts / 30 parts/hour = 9 hours.

Question 5

An employee earns $24.00 per hour for a standard 40-hour work week. For any hours worked beyond 40, the employee earns 1.5 times the standard hourly rate. How much does this employee earn for working 52 hours in one week?

  1. $1248.00
  2. $1392.00 (correct answer)
  3. $1404.00
  4. $1872.00
Explanation: This problem involves two rates. First, calculate the earnings for the standard 40 hours: 40 hours × $24.00/hour = $960.00. Next, determine the number of overtime hours: 52 hours - 40 hours = 12 overtime hours. Calculate the overtime rate: 1.5 × $24.00/hour = $36.00/hour. Calculate the overtime earnings: 12 hours × $36.00/hour = $432.00. Finally, add the standard and overtime earnings: $960.00 + $432.00 = $1392.00.

Question 6

The cost, C, in dollars, to produce n items at a factory is given by the equation C = 12n + 500.

Using the equation from the passage, what is the total cost to produce 300 items?

  1. $812.00
  2. $3,600.00
  3. $4,100.00 (correct answer)
  4. $15,600.00
Explanation: The equation C = 12n + 500 represents a constant rate of $12 per item (the variable cost) plus a fixed cost of $500. To find the total cost to produce 300 items, substitute n = 300 into the equation. C = 12(300) + 500. C = 3600 + 500. C = $4,100.00.

Question 7

A train travels the 210 miles between City A and City B in 3.5 hours. At the same constant speed, how long would it take the train to travel 330 miles?

  1. 4.5 hours
  2. 5.0 hours
  3. 5.5 hours (correct answer)
  4. 6.0 hours
Explanation: First, calculate the constant speed (rate) of the train. Speed = Distance / Time = 210 miles / 3.5 hours = 60 miles per hour. Now, use this speed to find the time it would take to travel 330 miles. Time = Distance / Speed = 330 miles / 60 mph = 5.5 hours.

Question 8

The temperature of a chemical solution is decreasing at a constant rate. Over a 25-minute period, it drops from 80°C to 45°C. What will the temperature of the solution be after the first 10 minutes of this period?

  1. 59°C
  2. 65°C
  3. 66°C (correct answer)
  4. 70°C
Explanation: First, find the total temperature change: 80°C - 45°C = 35°C. This change occurred over 25 minutes. The rate of cooling is 35°C / 25 minutes = 1.4°C per minute. Now, calculate the temperature drop after the first 10 minutes: 10 minutes × 1.4°C/minute = 14°C. Finally, subtract this drop from the initial temperature: 80°C - 14°C = 66°C.

Question 9

Maya and Ben are painting a fence. Working alone, Maya can paint the entire fence in 6 hours. Working alone, Ben can paint the same fence in 4 hours. If they start working together, what fraction of the fence will be painted after 1 hour?

  1. 110\frac{1}{10}
  2. 15\frac{1}{5}
  3. 512\frac{5}{12} (correct answer)
  4. 25\frac{2}{5}
Explanation: First, determine the rate of work for each person as a fraction of the fence painted per hour. Maya's rate is 16\frac{1}{6} of the fence per hour. Ben's rate is 14\frac{1}{4} of the fence per hour. When they work together, their rates add. Their combined rate is 16+14\frac{1}{6} + \frac{1}{4}. To add these fractions, find a common denominator, which is 12. 212+312=512\frac{2}{12} + \frac{3}{12} = \frac{5}{12}. This means that together they can paint 512\frac{5}{12} of the fence in one hour.

Question 10

A long-distance runner maintains a constant pace of 8 minutes per mile. The runner plans to take two 5-minute breaks during a marathon of 26.2 miles. What is the runner's total time from start to finish, including breaks?

  1. 3 hours, 29.6 minutes
  2. 3 hours, 39.6 minutes (correct answer)
  3. 3 hours, 45.0 minutes
  4. 4 hours, 9.6 minutes
Explanation: First, calculate the total running time. Running time = Pace × Distance = 8 minutes/mile × 26.2 miles = 209.6 minutes. Next, add the total break time. Total breaks = 2 breaks × 5 minutes/break = 10 minutes. The total time from start to finish is the sum of the running time and the break time: Total time = 209.6 minutes + 10 minutes = 219.6 minutes. Finally, convert this to hours and minutes. 219.6 minutes / 60 minutes/hour = 3 with a remainder. 3 hours = 3 × 60 = 180 minutes. The remaining minutes are 219.6 - 180 = 39.6 minutes. So the total time is 3 hours, 39.6 minutes.

Question 11

The value of a certain stock increased at a constant rate over a period. On Monday, its value was $32.50. By Wednesday of the same week, its value was $33.70. If the stock continues to increase at the same rate, what will its value be on Friday of that week?

  1. $34.30
  2. $34.90 (correct answer)
  3. $35.50
  4. $36.10
Explanation: First, find the rate of increase per day. The time from Monday to Wednesday is 2 days. The increase in value was $33.70 - $32.50 = $1.20. The rate is $1.20 / 2 days = $0.60 per day. The time from Wednesday to Friday is another 2 days. The additional increase will be 2 days × $0.60/day = $1.20. The value on Friday will be the value on Wednesday plus this additional increase: $33.70 + $1.20 = $34.90.

Question 12

A snail moves at a constant rate of 2 centimeters per minute. An ant starts at the same point 5 minutes after the snail and moves in the same direction at a constant rate of 10 centimeters per minute. How far from the starting point will the ant catch up to the snail?

  1. 10.0 cm
  2. 12.5 cm (correct answer)
  3. 15.0 cm
  4. 20.0 cm
Explanation: First, find the head start distance of the snail. In 5 minutes, the snail travels 5 min × 2 cm/min = 10 cm. The ant gains on the snail at a rate of 10 cm/min - 2 cm/min = 8 cm/min. The time for the ant to catch up is Time = Head Start Distance / Relative Speed = 10 cm / 8 cm/min = 1.25 minutes. The question asks for the distance from the starting point where they meet. This is the distance the ant travels in that time. Distance = Ant's Speed × Time = 10 cm/min × 1.25 min = 12.5 cm.

Question 13

A car travels for 2 hours at a constant speed of 60 mph and then for 3 hours at a constant speed of 40 mph. What is the total distance traveled by the car?

  1. 200 miles
  2. 240 miles (correct answer)
  3. 250 miles
  4. 260 miles
Explanation: This problem requires calculating the distance for each part of the journey and then adding them. Distance for the first part: Distance = Speed × Time = 60 mph × 2 hours = 120 miles. Distance for the second part: Distance = Speed × Time = 40 mph × 3 hours = 120 miles. The total distance is the sum of the two parts: 120 miles + 120 miles = 240 miles.

Question 14

A city bus arrives at a certain stop every 25 minutes. If a bus just departed at 2:10 PM, at what time will the fourth bus to arrive after the 2:10 PM departure get to the stop?

  1. 3:25 PM
  2. 3:50 PM (correct answer)
  3. 4:00 PM
  4. 4:15 PM
Explanation: The problem asks for the arrival time of the fourth bus after the 2:10 PM departure. This means we need to account for four 25-minute intervals. The total time that will pass is 4 × 25 minutes = 100 minutes. To find the arrival time, add 100 minutes to 2:10 PM. 100 minutes is equal to 1 hour and 40 minutes. Adding 1 hour to 2:10 PM gives 3:10 PM. Adding the remaining 40 minutes to 3:10 PM gives 3:50 PM.

Question 15

A recipe that serves 6 people requires 4 cups of flour. A caterer is preparing this recipe to serve 45 people. If the relationship between the number of people and the amount of flour is based on a constant rate, how many cups of flour will the caterer need?

  1. 24 cups
  2. 30 cups (correct answer)
  3. 36 cups
  4. 40 cups
Explanation: This is a proportion problem. First, find the rate of flour per person: 4 cups / 6 people = 23\frac{2}{3} cups per person. Then, multiply this rate by the desired number of servings: (23\frac{2}{3} cups/person) × 45 people = 2 × 15 = 30 cups. Alternatively, set up a proportion: 4 cups6 people=x cups45 people\frac{4 \text{ cups}}{6 \text{ people}} = \frac{x \text{ cups}}{45 \text{ people}}. Cross-multiply: 6x=4×456x = 4 \times 45, so 6x=1806x = 180. Divide by 6: x=30x = 30 cups.

Question 16

A 20-gallon container has a leak and loses water at a constant rate of 2.5 fluid ounces per minute. If the container is initially full, approximately how many hours will it take for the container to be one-quarter full? (1 gallon = 128 fluid ounces)

  1. 8.5 hours
  2. 10.7 hours
  3. 12.8 hours (correct answer)
  4. 17.1 hours
Explanation: First, determine the volume of water that must be lost for the container to be one-quarter full. This is three-quarters of the total volume: 3/4 × 20 gallons = 15 gallons. Next, convert this volume to fluid ounces: 15 gallons × 128 ounces/gallon = 1,920 ounces. Now, calculate the time in minutes it will take to lose this amount of water: Time (minutes) = 1,920 ounces ÷ 2.5 ounces/minute = 768 minutes. Finally, convert the time from minutes to hours: 768 minutes ÷ 60 minutes/hour = 12.8 hours.

Question 17

A delivery truck travels at a constant speed of 50 miles per hour. The driver makes a 45-minute stop for a delivery. If the total distance of the trip is 125 miles, what is the total time elapsed from the beginning of the drive to the completion of the stop?

  1. 2 hours, 30 minutes
  2. 2 hours, 50 minutes
  3. 3 hours, 15 minutes (correct answer)
  4. 3 hours, 30 minutes
Explanation: First, calculate the driving time. Time = Distance / Speed. Driving time = 125 miles / 50 mph = 2.5 hours. Convert 0.5 hours to minutes: 0.5 hours * 60 minutes/hour = 30 minutes. So, the driving time is 2 hours and 30 minutes. The driver also makes a 45-minute stop. The total elapsed time is the sum of the driving time and the stop time. Total time = (2 hours 30 minutes) + 45 minutes = 2 hours 75 minutes. Since 60 minutes equals 1 hour, 75 minutes is 1 hour and 15 minutes. So, the total time is 2 hours + 1 hour 15 minutes = 3 hours 15 minutes.

Question 18

A pool containing 12,000 gallons of water is being drained at a constant rate of 40 gallons per minute. However, a hose is simultaneously adding water to the pool at a constant rate of 15 gallons per minute. How many hours will it take for the pool to be completely empty?

  1. 4.17 hours
  2. 8.0 hours (correct answer)
  3. 13.33 hours
  4. 20.0 hours
Explanation: First, determine the net rate at which water is leaving the pool. The net drain rate is the drain rate minus the fill rate: 40 gal/min - 15 gal/min = 25 gal/min. This is the effective rate at which the volume is decreasing. Next, calculate the total time in minutes to empty the 12,000-gallon pool: Time (minutes) = 12,000 gallons / 25 gal/min = 480 minutes. The question asks for the time in hours, so convert minutes to hours: 480 minutes / 60 minutes/hour = 8.0 hours.

Question 19

A leaky faucet drips water at a constant rate, filling a 200-milliliter beaker in 40 minutes. At this rate, how many liters of water will drip from the faucet in a 24-hour period? (1 liter = 1,000 milliliters)

  1. 7.2 liters (correct answer)
  2. 12.0 liters
  3. 48.0 liters
  4. 72.0 liters
Explanation: First, find the drip rate in milliliters per minute: 200 mL / 40 min = 5 mL/min. Next, calculate the total number of minutes in a 24-hour period: 24 hours × 60 minutes/hour = 1,440 minutes. Now, calculate the total volume of water dripped in 24 hours: 5 mL/min × 1,440 min = 7,200 mL. Finally, convert this volume from milliliters to liters by dividing by 1,000: 7,200 mL / 1,000 mL/L = 7.2 liters.

Question 20

A company's profits increased at a constant rate from $1.2 million in 2015 to $2.7 million in 2020. If this rate continues, what is the projected profit for the year 2024?

  1. $3.6 million
  2. $3.9 million (correct answer)
  3. $4.1 million
  4. $4.2 million
Explanation: First, find the rate of profit increase per year. The time period is from 2015 to 2020, which is 5 years. The total increase in profit is $2.7 million - $1.2 million = $1.5 million. The rate of increase is $1.5 million / 5 years = $0.3 million per year. The year 2024 is 4 years after 2020. The projected increase in profit over these 4 years is 4 years × $0.3 million/year = $1.2 million. The projected profit for 2024 is the profit from 2020 plus this increase: $2.7 million + $1.2 million = $3.9 million.