# How to Find the Average Speed?

Lot of students gets confused while finding out the average speed, when various distances are travelled with different speed. Say for example, trip to Agra from Delhi is made at an average speed of 40 km/hr and the trip back at an average speed of 60 km/hr. Find their average speed for the entire trip. (Hint: It’s Not 50 Km/hr)

Rule: If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr, then the average speed during the whole journey is given by 2xy/x + y km/hr.

Or, If a person travels half the distance at a speed of x km/hr and the other half at a speed of y km/hr, then the average speed during the whole journey is given by 2xy/x + y km/hr.

So answer to the above question:

(2*60*40)/(60+40)  = 48 Km/hr

If a person travels three equal distances at a speed of x km/hr, y km/hr and z km/hr respectively, then the average speed during the whole journey is 3xyz/xy + yz + xz km/hr.

This problem can also be dealt with assuming some hypothetical distance.

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If you’ve a question related to time and speed or any other topic in maths, you can post it on QuickerMaths.com’s question answer platform #### Vineet Patawari

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## 3 thoughts to “How to Find the Average Speed?”

1. Ankit Arora says:

We can also explain this with H.P ( Harmonic progressions)

if 2 equal distance are covered with speeds a, and b
Then the avg speed is harmonic mean of a and b.
so avg speed = 2/(1/a + 1/b)

This can be extended to any number of distances
So if you have a person who is going with speeds a,b,c,d…. over equal distances, d,d,d,… upto n

then the avg speed will be :

n/ ( 1/a + 1/b + 1/c + 1/d + ……………)

and so on..

This can be used to find avg speed over 3 equal distance. if speeds are a,b,c, for 3 equal distances, then avg speed will be:
H.M. of a,b,c, ( HM means harmonic mean)

= 3/ (1/a + 1/b + 1/c )

2. Vedic Maths says:

Thanks Ravi 🙂

3. Ravi says:

nice work