Police Test Study Guide Police Written Test

Police Math Prep | Distance, Speed, and Time!

Mar 10th, 2020
police math prep

Police Math Prep Guide

Math is one of the most challenging parts of the police test. With enough practice, there is no reason why you can’t dominate this part of the exam. Today, we review police math prep that focuses on time, speed, and distance.

Police test questions on time, speed, and distance are common. As a police officer, these three factors come into play daily. You must have a thorough understanding of each concept – as well as knowing how to calculate speed, distance, and time when given only two of these metrics. We review some sample police questions below to assist you in this goal.

Of course, that isn’t the only reason why these questions are asked.

To make it through to the police academy, candidates must score high. Given the intense competition for places, it’s vital that candidates invest their best effort to make it to the top. It’s not enough to come in the bottom 50 percent who pass. You must prove to the police department that you mean business.

That’s why math is tested.

It tests the logical reasoning skills behind the candidate. Logical reasoning is a transferable skill. If you can perform well in math, it means that you can apply logical reasoning to other aspects of your career. This is very attractive for police departments as it gives them an active insight into your current logical reasoning skills.

Whilst your knowledge and application of math may be poor now, it is something you can train, like a muscle.

There are two ways to train this “muscle”:

  • To understand the meaning of police math questions – namely, what the question is asking you to do.
  • To practice as many math questions as you can – practicing your strengths, learning from your mistakes, and covering all tested topics.

One of the subjects that always comes up on the police math test is time, speed, and distance.

That’s the topic we focus on today – how to understand what the question is asking and how to use details provided in the question to answer that question.

Let’s get started.

Understanding Time, Speed, and Distance


Speed is a measure of how fast or slow something moves.

Speed is calculated by dividing the distance covered by the time it took to take to cover that distance.

In other words, speed = distance / time

Q. A police car travels 60 miles in 3 hours. What is the average speed of the police car?

As we have learned, the formula for speed is distance/time.

In this case, 60 miles / 3 hours = 20 miles per hour = 20 m/hr

m/hr is referred to as a compound unit – a combination of two units: both miles and hour. Of course, the police car won’t always drive at 20 miles per hour; the speed will fluctuate with time. Therefore, this value of “20m/hr” is an average speed.

During the police test, you may be given additional information that has nothing to do with the question asked. For instance, the question may add details such as, ”…of a 120 mile journey”. These are irrelevant details that will not be used to answer the question. Instead, these details are added so that examiners can learn whether you can identify the correct figures to successfully answer the question.

To succeed at the police math test, you must be able to identify relevant figures.

Second – always make a special note of what units are used and how to convert from one unit to another.

For example: the question may say 180 minutes, but you are asked to provide an answer in hours only.


Remember, the formula for speed = distance / time.

We can re-arrange this formula to calculate distance.

Distance = speed x time

Q. A suspect attempts to deflect the police officer by throwing a sharp object at him at a speed of 12 meters per second that travels for a total of 5 seconds.

What distance was the object thrown at the officer?

We are asked to calculate the distance. We have been given the speed (12 meters per second) and time (5 seconds).

Distance = speed x time = 12 meters/second x 5 seconds = 60 meters.

Again, on the day of your exam, ignore any irrelevant information. If you are asked to calculate distance, you need only the speed of the object and the total time the object traveled. It doesn’t matter what the object is, the formula is always the same.


Police exam questions on time are also regularly featured.

To calculate time, we re-arrange the above formula one more time.

Time = distance / speed

Q. A police officer traveled a total distance of 105 miles at a speed of 15 miles per hour. How long did it take for the officer to complete his journey?

Now, we have been asked to calculate time, “how long did it take…?”.

Time, as we have learned, is distance divided by speed.

In this case, 105 miles / 15 miles per hour = 7 hours

Logically, this makes sense.

If the officer is driving at 15 miles every hour, then after 2 hours, he covers 30 miles, after 3 hours, 45 miles, and so on. If you aren’t sure of the answer, perhaps try this manual approach. It’s also a great way to eliminate any potential wrong answers for multiple-choice questions on the police written test.


In summary, then, there are three key formulas to remember in this arena of police math prep:

  • Speed = distance x time
  • Distance = speed / time
  • Time = distance / speed

And remember the key points we raised in this lesson:

  • Identify what the question is asking
  • Identify the correct figures to use to answer the question
  • Ignore any details that are irrelevant to answering the question
  • Make sure units are correct – miles, minutes, hour

The more police math questions you practice, the easier it becomes to commit these details to memory and to maximize your result on the day of your exam. 

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