Average Speed Formula: Step-by-Step Methods and Examples

What is average speed?

Average speed is a compound measure that describes how fast an object travels over an entire trip. It smooths out any variations, such as accelerating, slowing down, or stopping, by treating the journey as one continuous movement.

To use this, you must understand standard speed distance time relationships. The formula is:

$\text{Average speed} = \dfrac{\text{total distance}}{\text{total time}}$

Standard units include meters per second ($\text{m/s}$), kilometers per hour ($\text{km/h}$), and miles per hour ($\text{mph}$). Average speed is a specific rate that describes the distance covered per unit of time.

Use total distance and total time

To find the correct average speed, you must aggregate the entire journey. You cannot simply find the mean of different speeds unless the time spent at each speed is exactly the same.

Always calculate the overall sum of the distances and the overall sum of the times. It functions as a unit rate for the whole trip, representing the equivalent steady pace.

Calculate a one-part journey

For a continuous journey without breaks or changes in given information, apply the formula directly.

1. Identify the total distance from the given information.
2. Identify the total time taken.
3. Ensure the units match the required speed unit.
4. Divide the total distance by the total time.

When given the average speed and asked to find a missing distance or time, rearrange the formula:

• $\text{Total distance} = \text{Average speed} \times \text{Total time}$
  
• $\text{Total time} = \dfrac{\text{Total distance}}{\text{Average speed}}$

Calculate a multi-part journey

When a journey consists of different legs, stops, or changing speeds, evaluate each part separately before using the final formula.

1. Identify known distances, times, and speeds for each part of the journey.
2. Use $\text{distance} = \text{speed} \times \text{time}$ or $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ to find any missing values for individual sections.
3. Add all individual distances to find the overall total distance.
4. Add all individual times, including any rest periods (where distance is $0$), to find the overall total time.
5. Divide the overall total distance by the overall total time.

Organizing the given information into a distance-time summary table helps prevent calculation errors.

Convert units consistently

A frequent cause of errors is mixing incompatible units. If you are calculating a speed in kilometers per hour, the distance must be in kilometers and the time must be strictly in hours.

Time is often given in hours and minutes. Because there are $60$ minutes in an hour, you must write the minutes as a fraction of $60$ to convert it to a decimal.

For example, $45$ minutes is $\dfrac{45}{60}$ of an hour, which simplifies to $\dfrac{3}{4}$ or $0.75$ hours. A time of $2$ hours and $15$ minutes must be entered into the formula as $2.25$ hours, never as $2.15$.

Worked examples

These types of math word problems require careful reading to extract the correct total values.

Example 1: Single one-part journey

Question: A train travels $240$ kilometers in $3$ hours and $12$ minutes. What is its average speed in $\text{km/h}$?

Method:

1. Convert the total time into hours. $12$ minutes is $\dfrac{12}{60}$ hours, which equals $0.2$ hours. The total time is $3.2$ hours.
2. Identify the total distance, which is $240\text{ km}$.
3. Divide the distance by the time.

$\text{Average speed} = \dfrac{240}{3.2}$

Answer: The average speed is $75\text{ km/h}$.

Check: Multiply the speed by the time to verify the distance: $75 \times 3.2 = 240\text{ km}$.

Example 2: Two-part journey

Question: A cyclist rides $30\text{ km}$ at a speed of $20\text{ km/h}$. She then changes her pace and rides another $15\text{ km}$ in $45$ minutes. What is her average speed for the whole journey?

Method:

1. Calculate the time for the first part of the journey. $\text{Time} = \dfrac{30}{20} = 1.5\text{ hours}$.
2. Convert the time for the second part into hours. $45$ minutes is $\dfrac{45}{60} = 0.75\text{ hours}$. The distance is given as $15\text{ km}$.
3. Find the total distance by adding the parts: $30 + 15 = 45\text{ km}$.
4. Find the total time by adding the times: $1.5 + 0.75 = 2.25\text{ hours}$.
5. Divide the total distance by the total time.

$\text{Average speed} = \dfrac{45}{2.25}$

Answer: The average speed is $20\text{ km/h}$.

Check: Multiply the final speed by the total time: $20 \times 2.25 = 45\text{ km}$, which matches the total distance.

Example 3: Counterexample with unequal travel times

Question: A car travels for $1$ hour at $40\text{ mph}$, and then travels for $3$ hours at $60\text{ mph}$. Show why the average speed is not $50\text{ mph}$.

Method:

1. If you incorrectly take the ordinary mean of the speeds, you get $\dfrac{40 + 60}{2} = 50\text{ mph}$.
2. Calculate the true total distance. Part 1 is $40 \times 1 = 40\text{ miles}$. Part 2 is $60 \times 3 = 180\text{ miles}$.
3. Add the distances to find the true total distance: $40 + 180 = 220\text{ miles}$.
4. Add the times to find the total time: $1 + 3 = 4\text{ hours}$.
5. Divide total distance by total time.

$\text{Average speed} = \dfrac{220}{4} = 55\text{ mph}$

Answer: The true average speed is $55\text{ mph}$.

Check: The true average is closer to $60\text{ mph}$ because the car spent three times as long traveling at that higher speed.

Common mistakes

Avoid these frequent errors when applying the formula.

Mistake: Averaging the separate speeds

Never take the ordinary arithmetic mean of two speeds unless the time spent traveling at each speed is identical. A speed of $30\text{ km/h}$ for one hour and $70\text{ km/h}$ for three hours does not result in an average speed of $50\text{ km/h}$. You must always find the overall total distance and divide by the overall total time.

Mistake: Incorrect decimal time

Treating hours and minutes as a standard decimal is incorrect. Writing $2$ hours and $20$ minutes as $2.2$ hours will produce the wrong answer, because $20$ minutes is $\dfrac{20}{60}$ or approximately $0.33$ hours, not $0.2$ hours.

Frequently asked questions

Clear up any remaining confusion with these common queries.

What is the difference between average speed and average velocity?

Average speed measures how fast an object covers its entire path, regardless of direction. Average velocity measures the overall change in position (displacement) divided by time, making it a vector that depends on direction.

Does average speed mean the object always traveled at that speed?

No. Average speed represents the constant pace required to complete the identical journey in the same time. The object's actual instantaneous speed might have been faster, slower, or zero during the trip.

Can I use the average speed formula if the journey includes a long rest?

Yes. A rest period adds to the total time but adds $0$ to the total distance. You must include the rest time in the denominator for the average speed to accurately reflect the whole journey.