# What is the caterpillar’s average speed over the entire journey?

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A caterpillar covers its outward journey to a vegetable patch at a speed of 114 metres per hour.

After filling up with his favourite foods the caterpillar returns, over exactly the same distance, at 38 metres per hour.

What is the caterpillar’s average speed over the entire journey?

posted Sep 2, 2016

Let the distance mentioned here be = D
Then D = 114 × T1 = 38 × T2
T1/T2 = 38/114 ( Note here that T2 is greater than T1 )
Now average speed is dependent on how speed the object is moving and for what length of time that speed is maintained.
Since the distance travelled in both the cases are same and there are 2 speeds here the slower speed will be coupled with longer time needed and vice versa.
So the average speed will be needing the ratio of the time of travel of each run to that of the total travel time in its calculations
.

There is also a shortcut for this. You can use the formula of harmonic mean for 2 terms ie., 2ab/(a+b) to get the same result. Here a and b are the 2 speeds. This works only if the distance travelled in both the cases are the same.

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