Police Math Scenario-Based Word Problems Flashcards

Officer Chen works a standard 40-hour week at a rate of $30 per hour. Any hours worked beyond 40 are paid at an overtime rate of 1.5 times the regular rate. During a holiday week, she worked a total of 48 hours and also received a flat $200 holiday bonus. What were her total gross earnings for that week?

Answer: $1,760

First, calculate the regular pay: 40 hours * $30/hour = $1,200. Next, determine the overtime hours: 48 - 40 = 8 hours. Calculate the overtime pay rate: $30 * 1.5 = $45/hour. Calculate the overtime earnings: 8 hours * $45/hour = $360. Finally, add all components together: $1,200 (regular) + $360 (overtime) + $200 (bonus) = $1,760.

A police department receives a community policing grant of $150,000. They allocate 30% to new surveillance equipment and 45% to officer training programs. From the remaining funds, they spend $12,500 on community outreach events. How much money from the grant is left unspent?

Answer: $25,000

First, calculate the total percentage allocated: 30% + 45% = 75%. Calculate the dollar amount for these allocations: 0.75 * $150,000 = $112,500. Find the remaining balance: $150,000 - $112,500 = $37,500. Finally, subtract the cost of the outreach events from this remainder: $37,500 - $12,500 = $25,000.

A patrol car has a 16-gallon fuel tank and averages 22 miles per gallon (MPG). An officer's standard patrol route is 44 miles long. If the officer starts with a full tank of gas, how many complete patrol routes can they finish before the tank is empty?

Answer: 8 routes

First, calculate the vehicle's total range on a full tank: 16 gallons * 22 MPG = 352 miles. Next, divide the total range by the length of one patrol route to find how many full routes can be completed: 352 miles / 44 miles per route = 8 routes.

An officer analyzes the response times for the last six emergency calls. The times, recorded in minutes, are: 11, 7, 14, 6, 18, 5. What is the median response time?

Answer: 9 minutes

To find the median, first arrange the numbers in ascending order: 5, 6, 7, 11, 14, 18. Since there is an even number of values (six), the median is the average of the two middle numbers (the 3rd and 4th values). Calculate the average of 7 and 11: (7 + 11) / 2 = 18 / 2 = 9 minutes.

An evidence locker contains 180 sealed packages of narcotics with an average weight of 400 grams per package. An additional package weighing 780 grams is added to the locker. Which of the following is the new average weight of all the packages?

Answer: 402 grams

First, find the total weight of the original packages: 180 packages * 400 grams/package = 72,000 grams. Add the weight of the new package: 72,000 grams + 780 grams = 72,780 grams. Determine the new total number of packages: 180 + 1 = 181. Finally, calculate the new average weight: 72,780 grams / 181 packages = 402 grams.

A precinct requires a minimum of 12 officers on duty. The staffing for Wednesday is as follows: - Day Shift: 16 officers scheduled, but 25% are out sick. - Evening Shift: 15 officers scheduled, but 3 call out sick. - Night Shift: 14 officers scheduled, but 3 call out sick. Which of the following shifts failed to meet the minimum staffing requirement?

Answer: Night Shift

Calculate the actual number of officers present for each shift: - Day Shift: 25% of 16 is 4. So, 16 - 4 = 12 officers. (Meets requirement). - Evening Shift: 15 - 3 = 12 officers. (Meets requirement). - Night Shift: 14 - 3 = 11 officers. (Fails to meet requirement). The Night Shift was the only one with fewer than 12 officers.