How Is Average Speed Calculated for a Round Trip with Different Speeds?

[realslow]

Homework Statement

If you drive from Physicsland to Chemistryland at a constant speed of 120 km/h and immediately return at a constant speed of 60.0 km/h, what is your average speed?

Homework Equations

The Attempt at a Solution

Somebody helped me out on this question and we used a weighted average.
(120 x 1/3) + (60 x 2/3) = 8.0 x 10^1 km/h
The answer is correct, but I don't understand how this weighted averaging works.
It would be great if you could help me understand!

 

[zhermes]

Naively you might guess that the average is 90 km/h right? The problem with that, is that it assumes you were driving for the same period of time at both speeds. In actuality, you were driving the same distance at both speeds. Therefore, you spent less time traveling at 120 km/h than traveling at 60 km/h. Therefore you need to weight 60 km/h more heavily.

Specifically, you were traveling at 60 km/h for twice as long (twice as long in time) as you were traveling at 120 km/h, thus you have to weight 60 by twice as much as 120. Because the total weight must add up to 1, the weights are 2/3 and 1/3.

Another way to think about it: say the distance between locations is 'd.' Solve for how long it takes (in hours) to travel that distance at the given speeds, and weight the speeds by that time (divided by the total time) to find the average.

Does that make sense?

 

[realslow]

Oh, I see!
Yes, it makes sense now :D
Thank you so much!

 

[ashishsinghal]

average speed = net distance / net time

dont confuse with mean of the speeds