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Arithmetic Speed distance time Converting units of time Substitution Rearranging equationsThis topic is relevant for:

Here we will learn about the average speed formula, including how to calculate the average speed and how to calculate the time or distance given the average speed.

There are also speed, distance and time worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.

The **average speed formula** is the formula used to calculate the average speed of a journey.

The average speed of an object is the total distance the object travels divided by the total amount of time taken.

Average speed is a **compound measure **which is usually given in the units metres per second (m/s), miles per hour (mph) or kilometres per hour (km/h).

We can calculate average speed using the formula,

\text{average speed } = \frac{\text{total distance}}{\text{total time}}.If we are calculating average speed in mph or km/h, we will need to ensure we have decimalised the time before we divide.

For example,

Nadine travels a distance of 84 \ km, in total it takes her 1 hour and 30 minutes.

To find her average speed we need to convert the time into a decimal before we can use the formula.

\begin{aligned} 1\text{ hour 30 minutes } &= 1 + \frac{30}{60}\text{ hours} \\\\ & \text{= 1}\text{.5 hours} \\\\ \end{aligned} \begin{aligned} \text{Average speed } &= \frac{\text{total distance}}{\text{total time}} \\\\ & =\frac{84}{1.5} \\\\ & =56\,\text{km/h} \end{aligned}We may need to calculate the average speed of a journey which has been broken into multiple parts.

For example,

Anne is on a journey which totals 250 miles.

She travels at 60 \ mph for 2 hours before taking a break for 30 minutes.

She travelled the remaining distance at a speed of 52 \ mph.

Calculate Anneβs average speed for the whole journey.

First we need to find how far Anne travelled in the first part of her journey.

Using the formula,

\begin{aligned} \text{distance} &= \text{speed }\times \text{ time} \\\\ & =60\times 2 \\\\ & =120 \ miles \end{aligned}Anne therefore has 250-120=130 miles remaining.

We next need to find the time taken for the last part of her journey.

Using the formula,

\begin{aligned} \text{time}&= \frac{\text{distance}}{\text{speed}} \\\\ & =\frac{130}{52} \\\\ & =2.5\,hours \end{aligned}We can now apply the average speed formula, ensuring we also include the time Anne took for a break.

\begin{aligned} \text{Average speed} &= \frac{\text{total distance}}{\text{total time}} \\\\ & =\frac{250}{2+0.5+2.5} \\\\ & =50\,mph \end{aligned}Anneβs average speed for the whole journey was 50 \ mph.

In order to use the average speed formula:

**Check what information about the journey has been provided.****Find any missing values required for the total distance and total time, including decimalisation of the time if required.****Substitute values into the formula**\textbf{average speed = }\frac{\textbf{total distance}}{\textbf{total time}}**and calculate.**

Get your free average speed formula worksheet of 20+ speed distance time questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free average speed formula worksheet of 20+ speed distance time questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE**Average speed formula** is part of our series of lessons to support revision on **compound measures**. You may find it helpful to start with the main compound measures lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Samiya drove from London to Glasgow. The journey took 8 hours 30 minutes and the total distance travelled was 415 miles. Find the average speed for her journey.

**Check what information about the journey has been provided.**

You have a total distance of 415 miles and a total time of 8 hours 30 minutes.

2**Find any missing values required for the total distance and total time, including decimalisation of the time if required.**

You need to decimalise the time of 8 hours 30 minutes.

\begin{aligned} 8\text{ hours } 30 \text{ minutes} &= 8 + \frac{30}{60}\text{ hours} \\\\ &= \text{ 8.5}\text{ hours} \end{aligned}3**Substitute values into the formula** \textbf{average speed = }\frac{\textbf{total distance}}{\textbf{total time}} **and calculate.**

Theo walked from home to school at an average speed of 4.8 \ km/h. It took him 45 minutes to walk to school. How far does Theo have to walk to school?

**Check what information about the journey has been provided.**

You have an average speed of 4.8 \ km/h and a total time of 45 minutes.

You need to decimalise the time of 45 minutes.

\begin{aligned} \text{45 minutes} &=\frac{45}{60}\text{ hours} \\\\ &= 0.75 \text{ hours} \end{aligned}

**Substitute values into the formula** \textbf{average speed = }\frac{\textbf{total distance}}{\textbf{total time}} **and calculate.**

Rearranging the formula you get,

\begin{aligned} \text{total distance} &= \text{average speed }\times \text{ total time} \\\\ & =4.8\times 0.75 \\\\ & =3.6\,km \end{aligned}

Dean cycled home from work at an average speed of 20 \ mph. He cycled a total of 12 miles. Find the total time it took Dean to cycle home in hours and minutes.

**Check what information about the journey has been provided.**

You have a total distance of 12 miles and an average speed of 20 \ mph.

You have the values you need for the formula.

** Substitute values into the formula** \textbf{average speed = }\frac{\textbf{total distance}}{\textbf{total time}}

Rearranging the formula you get,

\begin{aligned} \text{total time} &= \frac{\text{total distance}}{\text{average speed}} \\\\ & =\frac{12}{20} \\\\ & =0.6 \text{ hours} \\\\ \end{aligned}

0.6 hours is the same as \cfrac{2}{3} hours which is 40 minutes.

It took Dean 40 minutes to cycle home from work.

Charlotte drove to meet a friend for lunch. Her journey consisted of driving for 15 minutes at 30 \ mph, then 10 miles travelling at 50 \ mph. Find her average speed for the whole journey.

**Check what information about the journey has been provided.**

There are two parts to her journey. You have a time of 15 minutes and speed of 30 \ mph for the first part and a distance of 10 miles and a speed of 50 \ mph for the second part.

You need to find the total distance and the total time.

For the first part of the journey you can find the distance travelled.

15 minutes = 0.25 hours

\begin{aligned} \text{distance } &= \text{speed }\times \text{ time} \\\\ & =30\times 0.25 \\\\ & =7.5\,miles \end{aligned}

For the second part of the journey you can find the time taken.

\begin{aligned} \text{Time} &= \frac{\text{distance}}{\text{speed}} \\\\ & =\frac{10}{50} \\\\ & =0.2\,hours \end{aligned}

The total distance is 7.5 + 10 = 17.5 miles.

The total time is 0.25 + 0.2 = 0.45 hours

**Substitute values into the formula** \textbf{average speed = }\frac{\textbf{total distance}}{\textbf{total time}} **and calculate.**

\begin{aligned} \text{Average speed } &= \frac{\text{total distance}}{\text{total time}} \\\\ & =\frac{17.5}{0.45} \\\\ & =38.9 \ \text{mph} \end{aligned}

**The average speed shouldnβt be found by finding the mean of the different speeds**

A journey was broken into three parts and the speed for the three parts were 30 \ mph, \ 40 \ mph and 70 \ mph. A common error would be to find the average speed by finding the mean of 30, \ 40 and 70. This would not necessarily give the correct answer because we do not know the duration or distance of each part of the journey.

If the parts of the journey each had different durations, finding the mean of the values would not give the correct average speed. We need to find the **total time **and the **total distance**.

**The total time is not decimalised correctly**

A common error is to incorrectly decimalise time. 1 hour 30 minutes is **not** 1.3 hours.

1. A journey takes a total of 1 hour and 30 minutes and covers a distance of 90 miles. What was the average speed for the journey?

117 \ mph

60 \ mph

135 \ mph

69.23 \ mph

\begin{aligned}
\text{Average speed} &= \frac{\text{total distance}}{\text{total time}} \\\\
& =\frac{90}{1.5} \\\\
& =60\,\text{mph}
\end{aligned}

2. A journey takes a total of 3 hours and 45 minutes and covers a distance of 330 \ miles. What was the average speed for the journey?

95.65 \ mph

101.54 \ mph

88 \ mph

1237.5 \ mph

\begin{aligned}
\text{Average speed} &= \frac{\text{total distance}}{\text{total time}} \\\\
& =\frac{330}{3.75} \\\\
& =88\,\text{mph}
\end{aligned}

3. A journey has an average speed of 55 \ km/h. The total time taken was 4 hours and 24 minutes. Find the distance travelled.

242 \ km

233.3 \ km

220 \ km

12.5 \ km

\begin{aligned}
\text{Total distance} &= \text{average speed }\times \text{ total time} \\\\
& =55\times 4.4 \\\\
& =242 \ km
\end{aligned}

4. A journey of 120 \ km was completed with an average speed of 36 \ km/h. Find the time taken in hours and minutes.

3 hours 33 minutes

3.33 hours

3 hours 30 minutes

3 hours 20 minutes

\begin{aligned}
\text { Total time }&=\frac{\text { total distance }}{\text { average speed }} \\\\
\text { time }&=\frac{120}{36}=3.333 \ldots
\end{aligned}

3.333β¦ hours is 1\frac{1}{3} hours.

The total time taken is 1 hour 20 minutes.

5. A car travels at 30 \ mph for 20 minutes and then 54 \ mph for 40 minutes. Find the average speed for the whole journey.

46 \ mph

42 \ mph

84 \ mph

1.4 \ mph

This journey is in two parts. You need the total distance and the total time to calculate the average speed for the whole journey. For both parts you are given the speed and time.

You use these to find the distance travelled for each part.

\text {Distance} = \text {speed} \times \text {time}

Distance for part 1 is 30 \times \frac{20}{60}=10 miles.

Distance for part 2 is 54 \times \frac{40}{60}=36 miles.

The total distance is 10 + 36 = 46 miles.

The total time is 20 minutes + \ 40 minutes = 60 minutes = 1 hour.

The average speed for the whole journey is

\text { average speed }=\frac{\text { distance }}{\text { time }}=\frac{46}{1}=46 \ \mathrm{mph}.

6. A car travels 40 miles in 45 minutes before stopping for a 30 minute rest. It then travels at 60 \ mph for a further 51 minutes. Find the average speed for the whole journey.

56.875 \ mph

43.33β¦ \ mph

56.66β¦ \ mph

50 \ mph

This journey is in three parts. For part one you are given the distance and time. For the second part you are given the time at rest. For the third part you are given the speed and time.

You need the total distance and the total time to calculate the average speed for the whole journey.

\text {Distance} = \text {speed} \times \text {time}

Distance for part 1 is given in the question, 40 miles.

Distance for part 2 is given in the question, 0 miles.

Distance for part 3 is 60 \times \frac{51}{60}=51 miles.

The total distance is 40 + 0 + 51 = 91 miles.

The total time is 45 minutes + \ 30 minutes + 51 minutes = 126 minutes = 2.1 hour.

The average speed for the whole journey is

\text { average speed }=\frac{\text { distance }}{\text { time }}=\frac{91}{2.1}=43.33 . . \ \mathrm{mph}.

1. John drives from London to Liverpool via Birmingham.

The distance between London and Birmingham is 125 miles.

The distance between Birmingham and Liverpool is 100 miles.

John drives at an average speed of 50 \ mph between London and Birmingham. He plans to take a 30 minutes rest in Birmingham before driving to Liverpool.

It then takes him a further 4 hours to reach Liverpool due to bad traffic.

What is Johnβs average speed for the whole journey? Give your answer to 1 decimal place.

**(4 marks)**

Show answer

Method to find time taken from London to Birmingham. For example, 125 \div 50.

**(1)**

Time of 2.5 hours found.

**(1)**

Total distance ( 225 miles) and total time ( 7 hours).

**(1)**

Average speed of 32.1 \ mph.

**(1)**

2. Sarah leaves her house at 10:15 and drives to work 48 miles away.

She arrives at work at 11:09. The road between her house and work has a speed limit of 50 \ mph.

Has Sarah broken the speed limit?

**(3 marks)**

Show answer

Time of 54 minutes found.

**(1)**

**(1)**

53.333 \ mph and yes.

**(1)**

3. A journey is split into two parts. The first part of the journey is completed at an average speed of 45 \ km/h and takes 36 minutes.

The second part of the journey is 30 \ km. What speed must the second part of the journey be travelled at for the average speed for the whole journey to be 45.6 \ km/h?

Give your answer to 2 decimal places.

**(4 marks)**

Show answer

Distance of first part of journey found to be 27km.

**(1)**

Time needed for the whole journey found as 1.25 hours.

**(1)**

Method to find speed for second part (30 \div 0.65).

**(1)**

**(1)**

You have now learned how to:

- Use the average speed formula to find missing values from descriptions of a journey

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