Police Math Speed, Distance, and Time Questions and Answers

Question 1

An officer on patrol completes a 12.5-mile route in 30 minutes. What was the officer's average speed in miles per hour (MPH)?

Accepted Answer

25 MPH

Answer

The formula for speed is Speed = Distance / Time. First, convert the time from minutes to hours: 30 minutes = 0.5 hours. Then, divide the distance by the time in hours: 12.5 miles / 0.5 hours = 25 MPH.

Question 2

A suspect is fleeing at a constant speed of 80 MPH. If a pursuing officer maintains this speed for exactly 15 minutes, what is the total distance the officer has traveled?

Accepted Answer

20 miles

Answer

To find the distance, use the formula Distance = Speed × Time. The speed is in miles per hour, so the time must be converted from minutes to hours. 15 minutes is 1/4 or 0.25 of an hour. Multiply the speed by the time: 80 MPH × 0.25 hours = 20 miles.

Question 3

An officer needs to respond to a scene. The first part of the journey is 10 miles through city streets at an average of 20 MPH. The second part is 30 miles on a highway at an average of 60 MPH. What is the total time taken for the entire journey?

Accepted Answer

75 minutes

Answer

Calculate the time for each segment separately using Time = Distance / Speed, then add them together. City segment: 10 miles / 20 MPH = 0.5 hours. Highway segment: 30 miles / 60 MPH = 0.5 hours. Total time = 0.5 hours + 0.5 hours = 1 hour. Convert to minutes: 1 hour * 60 minutes/hour = 60 minutes. Wait, my math was off. Let me re-calculate. City: 10/20 = 0.5 hours. Highway: 30/60 = 0.5 hours. Total time = 0.5 + 0.5 = 1 hour. 1 hour is 60 minutes. Let me re-check the question and my distractors. Let's adjust the question. Highway part is 15 miles at 60 MPH. Time = 15/60 = 0.25 hours. Total time = 0.5 + 0.25 = 0.75 hours. 0.75 hours * 60 minutes/hour = 45 minutes. Okay, let me rewrite the question with the new numbers for clarity. New question: An officer responds to a call, driving 10 miles through the city at 20 MPH and then 15 miles on the highway at 60 MPH. What is the total travel time? Explanation: City time = 10 miles / 20 MPH = 0.5 hours. Highway time = 15 miles / 60 MPH = 0.25 hours. Total time = 0.5 + 0.25 = 0.75 hours. To convert to minutes: 0.75 hours * 60 minutes/hour = 45 minutes. Okay, now let me adjust the answers and explanation. Final Answer: Total time = 1 hour. My previous calculation was correct. Let me re-read the calculation one more time: City: 10 miles / 20 MPH = 0.5 hours. Highway: 30 miles / 60 MPH = 0.5 hours. Total time = 0.5 + 0.5 = 1.0 hours. 1.0 hours * 60 = 60 minutes. The correct answer should be 60 minutes. I will set the correct index and explanation for 60 minutes. My previous draft had an error. Final Check: City segment: Time = 10 miles / 20 MPH = 0.5 hours. Highway segment: Time = 30 miles / 60 MPH = 0.5 hours. Total Time = 0.5 hours + 0.5 hours = 1 hour. 1 hour is equal to 60 minutes.

Question 4

A speeding car is traveling at 90 MPH. A patrol car, positioned 0.5 miles behind the speeder, begins pursuit at a constant speed of 100 MPH. How long will it take the patrol car to catch up to the speeding car?

Accepted Answer

3 minutes

Answer

This is a relative speed problem. The patrol car is gaining on the speeder at a rate of 100 MPH - 90 MPH = 10 MPH. To find the time it takes to close the 0.5-mile gap, use the formula Time = Distance / Relative Speed. Time = 0.5 miles / 10 MPH = 0.05 hours. To convert this to minutes, multiply by 60: 0.05 hours * 60 minutes/hour = 3 minutes.

Question 5

A detective needs to travel to a crime scene 75 miles away. Which of the following scenarios results in the SHORTEST travel time?

Accepted Answer

Driving at an average speed of 50 MPH.

Answer

To compare the options, calculate the time for each. Option A is 1.5 hours = 90 minutes. Option B: Time = 75 miles / 45 MPH = 1.67 hours = 100 minutes. Option C: Time = 75 miles / 50 MPH = 1.5 hours = 90 minutes. Option D is 100 minutes. Comparing the times: 90 minutes, 100 minutes, 90 minutes, 100 minutes. Both A and C result in 90 minutes, which is the shortest time. In a single-best-answer format, this is problematic. Let me adjust the values. New values: A) Driving for 1.5 hours (90 min). B) Avg speed 60 MPH. C) Avg speed 55 MPH. D) Driving for 95 minutes. Calculations: A) 90 min. B) Time = 75 miles / 60 MPH = 1.25 hours = 75 minutes. C) Time = 75 miles / 55 MPH = 1.36 hours = ~82 minutes. D) 95 min. The shortest time is 75 minutes (Option B). This works.

Police Math Test Practice Test

Police Math Test Practice Test

Police Math Speed, Distance, and Time Questions and Answers