# Solve speed, distance and time problems

## Home learning focus

Learn about the relationship between speed, distance and time and how to solve problems involving them.

This lesson includes:

- two videos
- a learning summary
- three activities with answers

# Learn

## Understanding speed, distance and time

**Speed** tells us how fast something or someone is travelling. You can find the average speed of an object if you know the **distance** travelled and the **time** a journey took.

Speed, distance and time are called **variables** because they are affected by each other and therefore vary when another of them changes.

### Using formulae

Calculations involving speed, distance and time can be worked out using **formulae**, which can model real-life situations.

For example, the formula for speed is:

speed = distance ÷ time

The **formula triangle** is a quick way to remember how to calculate speed, distance or time.

When using the triangle you cover up the **variable** being calculated. Variables that are *next to* each other are **multiplied**. Variables that are *under* each other are **divided**.

Just like any other equation, the formula above can be rearranged, so by looking at the formula triangle you can logically work out:

distance = speed × time

time = distance ÷ speed

To calculate one of the variables, you always need the other two.

Watch this short video from BBC Bitesize, KS3 Maths to see an example of how to work out speed, distance and time. Think about how you would perform the calculation yourself.

## Units of speed

The **units** used to represent speed are linked to those for time and distance, and must be used consistently to represent values.

In the example in the video the distance was in millimetres (mm) and time was in seconds (s), meaning the units were in **millimetres per second (m/s).**

Other examples you are likely to see are:

distance = m (metres); time = s (seconds); speed = m/s (metres per second)

distance = km (kilometres); time = h (hours); speed = km/h (kilometres per hour)

** Example - Going for a run**

Be careful when you are working out problems where the information you have already been given is represented in **hours**.

Imagine that Kelly runs from 4:50pm until 5:20pm at an average speed of 7 km/h.

How can you work out how far she went?

- 4:50pm → 5:20pm = 30 minutes

However, the speed is given in **km/h**, so the time must be given in hours.

- 30 minutes = 0.5 hour

As you know, **distance = speed × time**. Look at the triangle for calculating distance above.

Distance = 7 x 0.5

Therefore, distance = 3.5 km

Kelly ran 3.5 km

## Converting compound measures

Speed is a **compound measure** - its units (eg m/s, km/hr) are a combination of both the units for distance and the units for time.

Sometimes, you'll be asked to convert between one unit of speed and another. Watch this video from Pearson which explains compound measures further and how to convert units of distance and time.

# Practise

## Activity 1

**Formula quiz**

So, think you know about using formulae in speed, distance and time calculations? Test your knowledge with this short quick-fire quiz, without looking above for any answers!

## Activity 2

**Interactive activity - speed, distance and time**

Have a go at this interactive activity from MyMaths, Oxford University Press to test your skills in solving speed, distance and time problems. Click the 'Practice' button to enter. You can mark your answers within the activity.

## Activity 3

**Speed, distance and time problems - mixed practice**

Now try solving these various problems involving speed, distance and time in this worksheet from Pearson, Maths Progress Second Edition. Write your answers on a piece of paper.

Click here to see the correct answers to the questions.

# There's more to learn

Have a look at these other resources around the BBC and the web.