# Average Speed Formula: Examples and Solutions!

The Average Speed Formula is a fundamental concept in motion. Moreover, it allows us to calculate the constant speed at which an object would have travelled to cover a certain distance in a specific time, even if the object’s actual speed varied throughout the journey. Read on to learn more about the Average Speed Formula as well as its use when there are two, three and four speeds given in the problem, along with examples and solutions.

## What is the Formula for Average Speed?

Furthermore, the Average Speed Formula equation is:

Average Speed = Total Distance / Total Time

In this Formula:

• Average Speed is represented by the symbol ‘S’ and is typically measured in units like kilometres per hour (km/h), meters per second (m/s), or miles per hour (mph).
• Total Distance (D) refers to the entire distance travelled by the object. Additionally, this distance is a scalar quantity which means that it only has magnitude and not direction.
• Total Time (T) represents the total duration the object took to cover the distance.

For instance, if a car travels 120 kilometres in 2 hours, its average speed can be calculated as:

S = D / T

= 120 km / 2 h

= 60 km/h

Therefore, this implies that if the car had maintained a constant speed of 60 km/h throughout the journey, it would have covered the same distance (120 km) in the same time (2 hours).

## Average Speed Formula with Two Speeds

When an object or person travels at two different speeds, the average speed can be calculated using the following formula:

Average Speed = (d1 + d2) / (t1 + t2)

Where:

• d1 = distance travelled at the first speed
• d2 = distance travelled at the second speed
• t1 = time taken at the first speed
• t2 = time taken at the second speed

To use this formula, you need to know the distance and time for each of the two speeds.

Example:

Ben drives from his home to the beach at 40 mph and returns home at 60 mph. The total distance to the beach and back is 160 miles. What is Ben’s average speed for the entire trip?

Solution:

Speed to the beach (first half of the trip) = 40 mph

Speed returning home (second half of the trip) = 60 mph

Total Distance travelled = 160 miles

Average Speed = 2 x Speed1 x Speed2 / (Speed1 + Speed2)

Thus, Ben’s average speed for the entire trip, driving at 40 mph to the beach and 60 mph on the return journey, is 48 mph.

## Average Speed Formula with two speeds and the same distance

If the object or person travels at two different speeds but covers the same distance, the average speed can be calculated using the following formula:

Average Speed = 2 x d / (t1 + t2)

Where:

• d = the distance travelled
• t1 = time taken at the first speed
• t2 = time taken at the second speed

Moreover, this formula is useful when the total distance travelled is known, but the individual distances for each speed are not.

Example:

A person travels from town A to town B on a scooter at 17 km/hr and returns from town B to town A on a bicycle at 8 km/hr. The distance between the two towns is the same for both legs of the journey. What is the average speed for the entire round trip?

Solution:

• Speed from A to B (scooter) = 17 km/hr
• Speed from B to A (bicycle) = 8 km/hr

Average Speed = 2 x 17 x 8 / (17 + 8)

Average Speed = 272 / 25

Average Speed ≈ 10.88 km/hr

Therefore, the average speed for the entire round trip, where the person travels from town A to town B at 17 km/hr and returns from town B to town A at 8 km/hr over the same distance, is approximately 10.88 km/hr.

## Average Speed Formula With Three Speeds

When an object or person travels at three different speeds, the average speed can be calculated using the following formula:

Average Speed = (d1 + d2 + d3) / (t1 + t2 + t3)

Where:

• d1 = distance travelled at the first speed
• d2 = distance travelled at the second speed
• d3 = distance travelled at the third speed
• t1 = time taken at the first speed
• t2 = time taken at the second speed
• t3 = time taken at the third speed

In addition, this formula can be extended to any number of different speeds, as long as the corresponding distances and times are known.

Example:

A man covers three equal distances with speeds of 10 km/hr, 20 km/hr, and 30 km/hr respectively.

Solution:

• The distances covered are equal, let’s call it ‘x’ km.
• The speeds are 10 km/hr, 20 km/hr, and 30 km/hr.

Step 1: Calculate the time taken to cover the distance ‘x’ at each speed.

Time taken at 10 km/hr = x/10 hours

Time taken at 20 km/hr = x/20 hours

Time taken at 30 km/hr = x/30 hours

Step 2: Substitute the values in the average speed formula.

Average Speed = (x + x + x) / ((x/10) + (x/20) + (x/30))

Average Speed = 3x / (6x/60)

Average Speed = 180/11 km/hr

Therefore, the average speed when a man covers three equal distances with speeds of 10 km/hr, 20 km/hr, and 30 km/hr is 180/11 km/hr.

## Average Speed Formula With Four Speeds

When an object or person travels at four different speeds, the average speed can be calculated using the following formula:

Average Speed = (d1 + d2 + d3 + d4) / (t1 + t2 + t3 + t4)

Where:

• d1 = distance travelled at the first speed
• d2 = distance travelled at the second speed
• d3 = distance travelled at the third speed
• d4 = distance travelled at the fourth speed
• t1 = time taken at the first speed
• t2 = time taken at the second speed
• t3 = time taken at the third speed
• t4 = time taken at the fourth speed

Moreover, this formula can be used when the object or person travels at any number of different speeds, as long as the corresponding distances and times are known.

Example:

A car travels at the following speeds and times:

• Speed 1: 60 km/h for 2 hours
• Speed 2: 80 km/h for 1.5 hours
• Speed 3: 50 km/h for 3 hours
• Speed 4: 70 km/h for 1 hour

To calculate the average speed, we use the formula:

Average Speed = (d1 + d2 + d3 + d4) / (t1 + t2 + t3 + t4)

Where:

• d1, d2, d3, d4 are the distances travelled at each speed
• t1, t2, t3, t4 are the times taken at each speed

Solution:

• d1 = 60 km/h x 2 h = 120 km
• d2 = 80 km/h x 1.5 h = 120 km
• d3 = 50 km/h x 3 h = 150 km
• d4 = 70 km/h x 1 h = 70 km
• t1 = 2 h, t2 = 1.5 h, t3 = 3 h, t4 = 1 h

Average Speed = (120 + 120 + 150 + 70) / (2 + 1.5 + 3 + 1)

= 460 km / 7.5 h

= 61.33 km/h

Thus, the average speed of the car travelling at the four different speeds is 61.33 km/h.