Right Way To Find The Average Speed

What was the given data?

If you are finding average speed of 2 given speeds as (Speed 1 + Speed 2)/2 then you are getting tricked by questioner. The speed itself is a distance covered per unit i.e. Speed = Distance/Time. Calculating average speed like that means,you are doing like,

Average Speed = (Speed1 + Speed2)/2
                     
                      = (Distance1/Time1 + Distance 2/Time2)/2              
            
So you need to find the total distance traveled & the total time taken to complete the entire journey.It should be like,


Average Speed = Total Distance/Total Time

                       = (Distance1 + Distance2)/(Time1 + Time2)

In the given problem, let D be the distance traveled by car to the office. Let T1 be the time required to go to the office & T2 be the time to return back.

Since, Speed = Distance / Time, Time = Distance / Speed.

Hence, 

T1 = D / 20

T2 = D / 30

Now,

Total distance traveled =  D + D = 2D, Total Time taken = T1 + T2

Hence,

Average Speed = 2D / (T1 + T2)

Average Speed = 2D / (D/20 + D/30)

Average Speed = 2D / (50D/600)

Average Speed = 2D / (D / 12)

Average Speed = 24 miles/hr.  

Therefore, the average speed of the journey is 24 miles/hr not 25 miles/hr [(20 + 30)/2].