Police Math Speed, Distance, and Time Questions and Answers 1 — 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)?
- 12.5 MPH
- 375 MPH
- 25 MPH (Correct answer)
- 6.25 MPH
Correct answer: 25 MPH
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?
- 20 miles (Correct answer)
- 1200 miles
- 40 miles
- 5.33 miles
Correct answer: 20 miles
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?
- 45 minutes
- 60 minutes
- 30 minutes
- 75 minutes (Correct answer)
Correct answer: 75 minutes
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?
- 5 minutes
- 2 minutes
- 3 minutes (Correct answer)
- 1 minute
Correct answer: 3 minutes
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?
- Driving for 1.5 hours.
- Driving at an average speed of 45 MPH.
- Driving at an average speed of 50 MPH. (Correct answer)
- Driving for 100 minutes.
Correct answer: Driving at an average speed of 50 MPH.
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.
Question 6: An officer drives at 40 mph for 30 minutes and then at 60 mph for 45 minutes. What is the total distance traveled?
- 50 miles
- 100 miles
- 65 miles (Correct answer)
- 75 miles
Correct answer: 65 miles
Calculate the distance for each part of the journey separately using Distance = Speed x Time, then add them. Part 1: Convert 30 minutes to 0.5 hours. Distance = 40 mph * 0.5 hours = 20 miles. Part 2: Convert 45 minutes to 0.75 hours. Distance = 60 mph * 0.75 hours = 45 miles. Total distance = 20 miles + 45 miles = 65 miles.
Police Math Speed, Distance, and Time Questions and Answers 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)?