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

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.