Basic Mathematics Application Flashcards

A deputy responds to an incident 18 miles away. For the first 12 miles, the deputy travels at an average speed of 48 mph. For the remaining 6 miles, the deputy travels at an average speed of 36 mph. How many total minutes did it take the deputy to arrive at the scene?

Answer: 25 minutes

To solve this, calculate the time for each segment of the trip and add them together. The formula to use is Time = Distance / Speed. For the first segment: Time = 12 miles / 48 mph = 0.25 hours. To convert hours to minutes, multiply by 60: 0.25 * 60 = 15 minutes. For the second segment: Time = 6 miles / 36 mph = 1/6 of an hour. To convert to minutes: (1/6) * 60 = 10 minutes. The total time is the sum of the two segments: 15 minutes + 10 minutes = 25 minutes.

A sheriff's department seizes 450 grams of a suspicious powder. After a lab analysis, it is determined that 60% of the powder is an illegal substance. Of that illegal portion, 15% is identified as pure fentanyl. How many grams of pure fentanyl were seized?

Answer: 40.5 grams

This is a two-step percentage problem. First, calculate the weight of the illegal substance: 450 grams * 60% (or 0.60) = 270 grams. Next, calculate the weight of the fentanyl from the illegal substance portion: 270 grams * 15% (or 0.15) = 40.5 grams.

A deputy recorded the number of traffic citations issued each day over a five-day work week. The daily totals were 8, 11, 7, 14, and 10. What was the average number of citations issued per day?

Answer: 10

To find the average (or mean), you must sum all the values and then divide by the number of values. The sum of the citations is 8 + 11 + 7 + 14 + 10 = 50. There are 5 days (values), so you divide the sum by 5: 50 / 5 = 10. The average number of citations per day was 10.

A recovered stolen rifle measures 3 feet 7 inches in length. For the evidence property report, all measurements must be recorded in total inches. Which of the following is the correct measurement?

Answer: 43 inches

To convert feet to inches, you must know that there are 12 inches in 1 foot. First, convert the feet to inches: 3 feet * 12 inches/foot = 36 inches. Then, add the remaining inches to this total: 36 inches + 7 inches = 43 inches.

A patrol sector is a rectangle measuring 4 miles by 2.5 miles. What is the total area of the patrol sector in square miles?

Answer: 10 square miles

The area of a rectangle is calculated by multiplying its length by its width. In this scenario, Area = Length * Width. So, the calculation is 4 miles * 2.5 miles = 10 square miles.

A deputy works a total of 46 hours in one week. The department pays overtime at a rate of 1.5 times the regular hourly wage for any hours worked over 40. If the deputy's regular hourly wage is $28.00, what is the deputy's total gross pay for the week?

Answer: $1,372.00

First, calculate the regular pay for the first 40 hours: 40 hours * $28.00/hour = $1,120.00. Next, determine the number of overtime hours: 46 total hours - 40 regular hours = 6 overtime hours. Then, calculate the overtime pay rate: $28.00 * 1.5 = $42.00/hour. Calculate the total overtime pay: 6 hours * $42.00/hour = $252.00. Finally, add the regular pay and overtime pay together: $1,120.00 + $252.00 = $1,372.00.