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Average speed formula

Here you 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.

Students will first learn about average speed formula as part of algebra in high school.

What is the average speed formula?

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 meters per second $(m/s),$ miles per hour $(mph)$ or kilometers per hour $(km/h).$

You can calculate average speed using the formula,

\text{average speed = }\cfrac{\text{total distance}}{\text{total time}}

If you are calculating average speed in $mph$ or $km/h,$ you will need to ensure the time value is in hours before dividing.

For example,

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

To find her average speed, convert the $time$ to $hours$ and use the formula.

\begin{aligned} 1\text{ hour 30 minutes } &= 1 + \cfrac{30}{60}\text{ hours} \\\\ & = {1.5 \mathrm{~hours}} \end{aligned}

\begin{aligned}\text { Average speed } & =\cfrac{\text { total distance }}{\text { total time }} \\\\ & =\cfrac{84 \mathrm{~km}}{1.5 \mathrm{~hours}} \\\\ & =56 \mathrm{~km} / \mathrm{h} \end{aligned}

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Average speed from multiple parts of a journey

You may need to calculate the average speed of a journey which has been broken into multiple parts.

For example,

Jerome is on a journey which totals $250 \, miles.$

He travels at $60 \, mph$ for $2 \, hours$ before taking a break for $30 \, minutes.$

He traveled the remaining distance at a speed of $52 \, mph.$

Calculate Jerome’s average speed for the whole journey.

First you need to find how far Jerome traveled in the first part of his journey.

You can rearrange the formula to calculate the distance.

If you multiply both sides of the formula by ‘total time’,

\left(\text { Average speed }=\cfrac{\text { total distance }}{\text { total time }}\right) \times \text { total time }

You get the formula for distance.

\begin{aligned}\text { distance } & =\text { speed } \times \text { time. } \\\\ & =60 \mathrm{~mph} \times 2 \text { hours } \\\\ & =120 \text { miles } \end{aligned}

Jerome therefore has $250-120=130 \, miles$ remaining.

Next, find the time taken for the last part of his journey.

If you divide both sides of the formula by ‘speed’,

\cfrac{\text { distance }}{\text { speed }} = \cfrac{\text { speed } \times \text { time }}{\text { speed }}

\begin{aligned}\text { Using the formula time } & =\cfrac{\text { distance }}{\text { speed }} \\\\ & =\cfrac{130 \text { miles }}{52 \mathrm{~mph}} \\\\ & =2.5 \text { hours } \end{aligned}

You can now apply the average speed formula, ensuring you also include the time Jerome took for a break.

\text{Average speed } =\cfrac{\text { total distance }}{\text { total time }}

\begin{aligned} \quad \quad \quad \quad & =\cfrac{250 \text { miles }}{2 \text { hours }+0.5 \text { hours }+2.5 \text { hours }} \\\\ & =50 \mathrm{~mph} \end{aligned}

Jerome’s average speed for the whole journey was $50 \, mph.$

What is the average speed formula?

Common Core State Standards

How does this relate to high school math?

Algebra – Creating Equations (HS-A.CED.A.4)
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law $V=IR$ to highlight resistance $R.$

How to use the average speed formula

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, converting the time if required.
Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

Average speed formula examples

Example 1: calculating the average speed

Samiya drove from New York City to Roanoke, VA. The journey took $8\text{ hours 30 minutes }$ and the total distance traveled was $415 \, miles.$ Find the average speed for her journey.

Check what information about the journey has been provided.

There is a total distance of $415 \, miles$ and a total time of $8\text{ hours 30 minutes. }$

2Find any missing values required for the total distance and total time, converting the time if required.

You need to convert the time of $8\text{ hours 30 minutes }$ to just $hours.$

\begin{aligned} 8\text{ hours 30 minutes } & = 8 + \cfrac{30}{60}\text{ hours} \\\\ & = 8.5 \text{ hours} \end{aligned}

3Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

\text{Average speed } =\cfrac{\text { total distance }}{\text { total time }}

\begin{aligned} \;\; & =\cfrac{415 \text { miles }}{8.5 \text { hours }} \\\\ & =48.8 \mathrm{~mph} \text{ (rounded to the nearest tenth)} \end{aligned}

Example 2: calculating the total distance

The average speed of a car traveling round trip from Mumbai, India to Thane, India is $25 \, km/h.$ If the journey took $2 \, hours$ and $10 \, minutes,$ what distance was traveled?

Check what information about the journey has been provided.

There is an average speed of $25 \, km/h$ and an entire trip time of $2 \, hours$ and $10 \, minutes.$

Find any missing values required for the total distance and total time, converting the time if required.

You need to convert $2 \, hours$ and $10 \, minutes$ to just $hours.$

\begin{aligned} 2 \text { hours and 10 minutes } & = 2 \cfrac{10}{60} \mathrm{~hours} \\\\ & = 2.1 \overline{6} \mathrm{~hours} \end{aligned}

Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

Rearranging the formula you get,

\begin{aligned}\text { total distance } & =\text { average speed } \times \text { total time } \\\\ & =25 \mathrm{~kph} \times 2.1 \overline{6} \mathrm{~h} \\\\ & =54.1 \overline{6} \mathrm{~km} \end{aligned}

Example 3: calculating the total distance

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.

There is an average speed of $4.8 \, km/h$ and a total time of $45 \, minutes.$

Find any missing values required for the total distance and total time, converting the time if required.

You need to convert the time $45 \, minutes$ to $hours.$

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

Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

Rearranging the formula you get,

\begin{aligned}\text { total distance } & =\text { average speed } \times \text { total time } \\\\ & =4.8 \mathrm{~kph} \times 0.75 \mathrm{~h} \\\\ & =3.6 \mathrm{~km} \end{aligned}

Example 4: calculating the total time

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

Check what information about the journey has been provided.

There is a total distance of $20 \, miles$ and an average speed of $12 \, mph.$

Find any missing values required for the total distance and total time, converting the time if required.

You have the values you need for the formula.

Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

Rearranging the formula you get,

\begin{aligned} \text { total time }&=\cfrac{\text { total distance }}{\text { average speed }} \\\\ & =\cfrac{20}{12} \\\\ & =1 . \overline{6} \text { hours } \end{aligned}

$1 . \overline{6} \, hours$ is the same as $1 \cfrac{2}{3} \, hours$ which is $1 \, hour \, 40 \, minutes.$

It took Dean $1 \, hour \, 40 \, minutes$ to cycle home from work.

Example 5: calculating the average speed for a journey with multiple parts

Desirée drove to meet a friend for lunch. Her journey consisted of driving for $15 \, minutes$ at $30 \, mph,$ then $10 \, miles$ traveling 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. There is a time of $15 \, minutes$ and a speed of $30 \, mph$ for the first part and a distance of $10 \, miles$ and a speed of $50 \, mph$ for the second part.

Find any missing values required for the total distance and total time, converting the time if required.

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

For the first part of the journey, you can find the distance traveled.

\begin{aligned}15 \text { minutes } & = 0.25 \text { hours} \\\\ \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 } & =\cfrac{\text { distance }}{\text { speed }} \\\\ & =\cfrac{10 \text { miles }}{50 \mathrm{~mph}} \\\\ & =0.2 \text { 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, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

\text {Average speed } =\cfrac{\text { total distance }}{\text { total time }}

$\begin{aligned} \;\; & =\cfrac{17.5 \text { miles }}{0.45 \text { hours }} \\\\ & =38.9 \mathrm{~mph} \text { (rounded to the nearest tenth)} \end{aligned}$

Example 6: calculating the average speed for a journey with multiple parts

Tanner wants to meet a friend at the library. From his home to the library is a $15 \, minutes$ bike ride at $10 \, mph.$

Returning, he will walk with his friend at $6 \, mph.$ If Tanner and his friend stay at the library for $20 \, minutes,$ what is the average speed for Tanner’s roundtrip from the entire trip?

Check what information about the journey has been provided.

There are three parts to his journey. There is a time of $15 \, minutes$ and speed of $10 \, mph$ for the first part, $20 \, minutes$ of $0 \, mph$ at the library and the return trip home at $6 \, mph.$

Find any missing values required for the total distance and total time, converting the time if required.

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

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

\begin{aligned}15 \text { minutes } & =0.25 \text { hours } \\\\ \text { distance } & =\text { speed } \times \text { time } \\\\ & =10 \times 0.25 \\\\ & =2.5 \text { miles } \end{aligned}

The second part of the journey was spent at the library, so $0 \, miles$ were moved.

Converting the $20 \, minutes$ to $hours, \, \cfrac{20}{60},$ shows that they spent $0 . \overline{3} \, hours$ at the library.

For the third part of the journey you can find the time taken. You know from the first part of the journey, that the distance from the library to Tanner’s home is $2.5 \, miles.$

\begin{aligned}\text { Time } & =\cfrac{\text { distance }}{\text { speed }} \\\\ & =\cfrac{2.5 \text { miles }}{6 \mathrm{~mph}} \\\\ & =0.41 \overline{6} \text { hours } \end{aligned}

The total distance is $2.5+0+2.5=5 \, miles.$

The total time is $0.25+0 . \overline{3}+0.41 \overline{6}=1 \text { hour }$

Substitute values into the formula, $\textbf{ average speed }=\cfrac{\textbf{total distance}}{\textbf{total time}}$ and calculate.

\begin{aligned}\text { Average speed } & =\cfrac{\text { total distance }}{\text { total time }} \\\\ & =\cfrac{5 \text { miles }}{1 \text { hour }} \\\\ & =5 \mathrm{~mph} \end{aligned}

Teaching tips for average speed formula

Start with situations that have one speed, before moving on to ones that involve multiple time intervals with different speeds.

Provide activities that have students recording time and distance. This could be as simple as using a stopwatch to time each student walking $100 \, m.$ Or as advanced as using robotics equipment or GPS technology.

If using worksheets, make sure to choose ones that have a variety of units of time, units of distance and units of speed. They should also vary in what information is being solved for, such as the speed of the car, travel time, starting point, etc.

Easy mistakes to make

Creating the wrong units
Since speed is a compound unit, it is important to pay attention to the units in every calculation. Sometimes an equation creates a compound unit and sometimes it cancels out common units.

For example,
1. $\frac{20 \text { miles }}{2 \text { hours }}=10 \frac{\text { miles }}{\text { hour }} \leftarrow$ The equation sets up the units as $\frac{\text { miles }}{\text { hour, }}$ which is often represented as “miles per hour” or “mph”
2. $\frac{2.5 \mathrm{~miles}}{6 \mathrm{~mph}}=0.41 \overline{6} \text { hours } \leftarrow$ The equation sets up the units as
  $\frac{\text { miles }}{\text { mph }}=\frac{\text { miles }}{\frac{\text { miles }}{\text { hour }}}=\text { miles } \times \frac{\text { hour }}{\text { miles }}=\text { hour. }$ The units of miles cancel out, leaving ‘hours’.

Assuming instantaneous speed or constant speed for entire trip
An average speed of $30 \, mph$ does not automatically mean that the object was instantaneously going $30 \, mph$ at the start of the period of time.

It does not also mean that the object was traveling at exactly $30 \, mph$ for the total duration of the movement. Let’s look at two situations where $30 \, mph$ is the average speed.

$\quad 1)$ A car travels for $25 \, minutes$ at $30 \, mph$ the entire trip.
$\quad 2)$ A car travels for $25 \, minutes$ at $10 \, mph$ and then $25 \, minutes$ at $50 \, mph.$

Example # $2$ changes speeds, but still has an average of $30 \, mph.$

Finding the average speed from a journey with varying speeds by finding the mean value 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 you 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. You need to find the total time and the total distance.

Not converting the total time to hours correctly
A common error is to incorrectly convert time to hours.

For example,
$1 \, hour \, 30 \, minutes$ is not $1.3 \, hours$ .
To convert, write $1 \, hour \, 30 \, minutes$ as the mixed number $1 \cfrac{30}{60},$ where the numerator is the minutes passed and the denominator is the whole, in this case $60 \, minutes.$
Then write the mixed number as a decimal: $1 \cfrac{30}{60}=1.5$

Practice average speed formula questions

117 \, mph

60 \, mph

135 \, mph

69.23 \, mph

First, convert $1 \, hour$ and $30 \, minutes$ to just $hours.$

\begin{aligned} 1 \text { hour and 30 minutes } &=1 \cfrac{30}{60} \text { hours } \\\\ 1 \cfrac{30}{60} \, hours &=1.5 \, hours \end{aligned}

\begin{aligned} \text { Average speed }& =\cfrac{\text { total distance }}{\text { total time }} \\\\ & =\cfrac{90 \text { miles }}{1.5 \text { hours }} \\\\ & =60 \mathrm{~mph} \end{aligned}

95.65 \, mph

101.54 \, mph

88 \, mph

1,237.5 \, mph

First, convert $3 \, hours$ and $45 \, minutes$ to just $hours.$

\begin{aligned} 3 \text { hours and 45 minutes } &=3 \cfrac{45}{60} \text { hours } \\\\ 3 \cfrac{45}{60} \, hours &=3.75 \, hours \end{aligned}

\begin{aligned} \text { Average speed }& =\cfrac{\text { total distance }}{\text { total time }} \\\\ & =\cfrac{330 \text { miles }}{3.75 \text { hours }} \\\\ & =88 \mathrm{~mph} \end{aligned}

242 \, km

233.3 \, km

220 \, km

12.5 \, km

First, convert $4 \, hours$ and $24 \, minutes$ to just $hours.$

\begin{aligned} 4 \text { hours and 24 minutes } &=4 \cfrac{24}{60} \text { hours } \\\\ 4 \cfrac{24}{60} \, hours &=4.4 \, hours \end{aligned}

\text {Total distance } =\text { average speed } \times \text { total time }

\begin{aligned} \quad \quad \quad \quad & =55 \mathrm{~km} / \mathrm{h} \times 4.4 \mathrm{~h} \\\\ & =242 \mathrm{~km}\end{aligned}

3 \, hours \, 33 \, minutes

3.33 \, hours

3 \, hours \, 30 \, minutes

3 \, hours \, 20 \, minutes

\begin{aligned} \text { Total time }&=\cfrac{\text { total distance }}{\text { average speed }} \\\\ \text { time } & =\cfrac{120 \mathrm{~km}}{36 \mathrm{~km} / \mathrm{h}}=3 . \overline{3} \text { hours } \end{aligned}

$3 . \overline{3} \text { hours }$ is $1 \cfrac{1}{3} \text { hours }.$

The total time taken is $1 \, hour \, 20 \, minutes.$

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 traveled for each part.

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

Distance for part $1$ is $30 \mathrm{~mph} \times \cfrac{20}{60} \text { hours }=10 \text { miles. }$

Distance for part $2$ is $54 \mathrm{~mph} \times \cfrac{40}{60} \text { hours }=36 \text { miles }$

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 }=\cfrac{\text { distance }}{\text { time }}=\cfrac{46}{1}=46 \mathrm{~mph}.

56.875 \, mph

43 . \overline{3} \, mph

56 . \overline{6} \, 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 $60 \mathrm{~mph} \times \cfrac{51}{60} \text { hours }=51 \text { miles }$

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

The total time is
$45$ minutes $+ \, 30$ minutes $+ \, 51$ minutes $= 126$ minutes $= 2.1$ hours.

The average speed for the whole journey is

\text { average speed }=\cfrac{\text { distance }}{\text { time }}=\cfrac{91 \text { miles }}{2.1 \text { hours }}=43 . \overline{3} \mathrm{~mph}

Average speed formula FAQs

What is average velocity?

Average velocity is similar to average speed, but velocity accounts for direction.

What is the average speed equation?

The average speed equation is the same as the average speed formula, which is $\text { average speed }=\cfrac{\text { distance }}{\text { time. }}$

What is ‘avg’?

The abbreviation ‘avg’ is for the word average and it is sometimes used for average speed formula activities.

What are the SI units used for average speed calculation?

The base SI units for time and distance are seconds and meters, but hours and kilometers are often used for longer time and distance calculations.

What is a time graph?

This is one way to represent the time passed and distance traveled. It can also be used to calculate average speed.

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