Average Speed: 30km/hr Explained

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The average speed for a round trip where the outbound speed is 40 km/hr and the return speed is 60 km/hr is not simply the arithmetic average of the two speeds. Instead, the average speed is calculated by dividing the total distance by the total time taken for the trip. For a distance of 200 km each way, the total time is derived from the individual times for each leg of the journey. This results in an average speed of 30 km/hr, illustrating that the average speed can be significantly lower than the speeds for each segment. The discussion emphasizes that average speed calculations must consider the time spent traveling at each speed, rather than just averaging the speeds.
alex engler
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If the average speed going to town is 40km/hr, and return at an average speed of 60 km/hr. what is the average speed? why is it not 50 km/hr

Is the answer 30? because he goes 40 km/hr for 1 1/2 hours. etc.
 
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The average speed is found by dividing the total distance by the total time of travel. (Hint: Find expressions for the time for each leg of the trip in terms of its distance and speed.)
 
You can pretend the distance going to town is 200km. Now find the total distance of there and back, divided by the total time. So you must calculate the total time.

An easy way to understand this is pretend you are planning on going from point A to point B(which is 100km from point A). If you go there at 1000km/hr, it will only take you 6 minutes, and if you go back at .00001km/hr, it will take you a LONG time, so doesn't it make sense that your average speed would be quite low?
 
You are correct that the "average speed" is not the arithetic average (\frac{v_1+v_2}{2}) but any "average" of two numbers has to be between them!
 

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