**Chances are you’ll get at least one speed, distance and time problem in the Quantitative Reasoning subtest. With enough practice and a good idea of what to look out for when reading a question, these problems become easier to solve.**

Often found in text format, this type of question-type is one many students become quickly familiar with, so don’t get nervous if you don’t know how to approach it. In this article, we will explore the key skills needed for dealing with speed, distance and time problems in the UCAT quantitative reasoning. These are all basic skills and should be used as a guide to help recognise weak areas and structure targeted revision. I’ve done my best to keep this article straight to the point, however, if you would like tips, strategies and techniques to improve your accuracy and speed on this subject do check out the new UCAT Study Guide.

### Key Concepts: Definitions, Formula and Triangle

*Speed* is a measure of how quickly an object moves from one place to another. It is equal to the* distance* travelled divided by the* time*. It is possible to find any of these three values using the formula below:

The above formula can be rearranged to solve Distance and Time. As seen below:

An easy way to remember the formulae is to put distance, speed and time (or the letters D, S and T) into a triangle as seen below:

The way to use this triangle is as follows. Take your finger and cover up the letter which represents the thing that you’re trying to calculate. Then, the triangle will tell you what to do with the other two quantities to get the value you want.

**For example,** if we want to calculate the speed, then we construct this triangle and cover up the speed (since that’s what we want). Then, we see that what’s leftover is “distance over time”, or in other words, distance divided by time will give us the speed.

### Skill #1 – Calculating Speed

These are common in the quantitative reasoning subtest. However, never expect problems to be straight forward. Many of the times, examiners provide the distance and time in different units, which will require additional steps to solve the problem. Other times, you’ll need to solve for the average speed, that will have multiple parts before getting the final answer. For example, *Michael walks uphill to university for 45 minutes at just 8 km/hr. He then travelled back home along the same route **downhill at a speed of 24 km/hr. What is the average speed for the entire trip? *(Correct Answer is 12 km/hr. Be sure in the exam to expect an option with 16 km/hr to catch some students out).

A helpful tip is to glance at the answer options to double-check the units. For example, if the answers are in m/s but you’ve been given the distance in Kilometres and time in hours, then you know you need to do a conversion as an additional step.

Questions can also be presented in a graphical format where you are provided with a Distance-time graph and asked to work out the speed where the gradient of the line is equal to the speed of the object. When dealing with graphs, be sure to double-check the unit of the axis. For example, expect examiners to have answer options in km/hr, but the axis on the graph are different, e.g. are in Km (y-xis) and minutes (x-axis).

### Skill #2 – Calculating Distance

These problems are not as common as skill #1 but have come up in past UCAT tests. Make sure to double-check units, questions can present information in one unit, but answer options are in another. You may be presented with a speed-time graph (see below) where the question may ask you to deduce the distance covered.

Using geometry, the distance covered can be calculated by **finding the area under the line**. In the above diagram, that would be the *area of the triangle* + *areas of the square*. Be sure to double-check the unit of the graph’s axis is the same as answer options.

### Skill #3 – Calculating time

This is also common in the quantitative reasoning subtest. Many of the time, the units are different for distance or speed, and you may need to convert one or the other to derive an answer. Same as the above skills, double-check the unit of the answer options before solving the problem.

### Skill #4 – Dealing with Conversions

This is at the core of difficult speed, distance and time problems. Converting units isn’t difficult. It’s just that they can be easily missed and calculations can be time-consuming at times. If you can master this skill and are able to do conversions quickly, you should find all problems in relation to this topic pretty easy. Common conversions you can expect to do in the exam:

- Converting Kilometres (km) to metres (m) and vice versa
- Converting hours (hr) to minutes (mins) and vice versa
- Converting hours (hr) to seconds (sec) and vice versa
- Converting minutes (mins) to seconds (sec) and vice versa
- Converting Km/hr to m/s and vice versa
- Converting Km/sec to Km/hr and vice versa

### Skill #5 – Determining Acceleration

Acceleration is the rate of change in *speed* in a given *time*. It can be calculated by dividing the change in speed by the time taken for the change.

Expect questions in the graphical format, where you are given a speed-time graph (like the one above) and may be asked deduce the acceleration. This will be the **gradient of the line in the graph**. More difficult problems may have multiple parts before arriving at the final answer. Always be sure to check units as well.

### Top Tips for Dealing with Speed, Distance and Time Problems

#### 1. Avoid Common Mistakes

Some common mistakes to avoid when solving speed, distance and time problem:

- Using the wrong units
- Using the wrong formula
- Overcomplicating problem
- Doing too many conversions (best to convert the final answer as opposed to converting numbers as you go)

#### 2. Always glance at the answer options

Always glance at the answer options to double-check units, or potentially estimate the final answer.

#### 3. Always use conversion shortcuts when possible

Use shortcuts wherever possible. For example, converting speed from **km/h **to** m/s **is a simple as multiplying by 5/18. So 36 km/hr is 10 m/s. Try to learn some conversion shortcuts before test day.

#### 4. Do as much mental maths as possible

Speed, distance time problems in the UCAT are usually multiple-step calculations, so be sure to use mental maths whenever possible to save time.