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A man drives his car to the office at 20miles/hr. After reaching the
office, he realizes that it's a new year holiday so he went back home at
a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey?
Right way to calculate the average speed!
Source
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].
