PELLET B Mathematical Reasoning & Problem Solving 2 — Questions and Answers
Question 1: An officer drives 45 miles in 1.5 hours. What is the officer's average speed?
- 25 mph
- 30 mph (Correct answer)
- 35 mph
- 40 mph
Correct answer: 30 mph
Average speed = distance / time = 45 / 1.5 = 30 mph.
Average speed is calculated by dividing total distance by total time: 45 miles / 1.5 hours = 30 miles per hour. This is a fundamental calculation officers use when estimating travel times for patrol routes and analyzing accident reconstruction data.
Question 2: A police department has a budget of $2.4 million. If 35% goes to salaries and 20% to equipment, how much remains for other expenses?
- $1,080,000 (Correct answer)
- $1,200,000
- $960,000
- $840,000
Correct answer: $1,080,000
Salaries and equipment total 55%. Remaining: 45% of $2,400,000 = $1,080,000.
Combine known allocations: 35% + 20% = 55%. Remaining: 100% - 55% = 45%. Apply to budget: $2,400,000 x 0.45 = $1,080,000. Budget calculations are routine in law enforcement administration for resource allocation.
Question 3: If a crime rate of 12 per 1,000 residents drops by 25%, what is the new crime rate?
- 3 per 1,000
- 6 per 1,000
- 9 per 1,000 (Correct answer)
- 10 per 1,000
Correct answer: 9 per 1,000
25% of 12 is 3. New rate: 12 - 3 = 9 per 1,000 residents.
To find a 25% decrease: 12 x 0.25 = 3. Subtract: 12 - 3 = 9. Alternatively, 12 x 0.75 = 9. Understanding crime rate calculations is essential for analyzing CompStat reports and measuring effectiveness of prevention programs.
Question 4: An evidence room is 12 feet long, 8 feet wide, and 10 feet high. What is its volume in cubic feet?
- 240 cubic feet
- 480 cubic feet
- 720 cubic feet
- 960 cubic feet (Correct answer)
Correct answer: 960 cubic feet
Volume = length x width x height = 12 x 8 x 10 = 960 cubic feet.
Volume of a rectangular room: 12 x 8 x 10 = 960 cubic feet. Officers encounter similar calculations when planning evidence storage, determining room capacities, and working with building plans during tactical operations.
Question 5: During a 4-week period, an officer wrote 15, 22, 18, and 25 traffic citations. What is the average number per week?
- 18
- 19
- 20 (Correct answer)
- 21
Correct answer: 20
Average = (15 + 22 + 18 + 25) / 4 = 80 / 4 = 20.
The arithmetic mean: (15 + 22 + 18 + 25) = 80, then 80 / 4 = 20 citations per week. Calculating averages is fundamental in law enforcement performance reporting for evaluating productivity and identifying trends.
Question 6: A suspect is traveling at 80 mph while an officer is 10 miles behind traveling at 100 mph. How long will it take the officer to catch the suspect?
- 15 minutes
- 20 minutes
- 30 minutes (Correct answer)
- 45 minutes
Correct answer: 30 minutes
Closing speed = 100 - 80 = 20 mph. Time = 10 miles / 20 mph = 0.5 hours = 30 minutes.
The officer closes the gap at 100 - 80 = 20 mph. To cover 10 miles at 20 mph: 10 / 20 = 0.5 hours = 30 minutes. Pursuit-related calculations are directly relevant for estimating interception times and making tactical decisions.
PELLET B Mathematical Reasoning & Problem Solving 2
An officer drives 45 miles in 1.5 hours.
What is the officer's average speed?