Amortized Analysis: Find the Rate of Travel

Question

A biker can travel at 24kms per hour with the flow of the wind, but only 12kms per hour against the wind. Assuming the biker starts and finishes at the same point.

What is the rider's amortized rate of travel?

I do not understand how the answer is arrived at, I have read my lecture notes but it is a little confusing.

Thanks

Answer 1

I am assuming the biker goes from point A to point B, and then back from point B to point A, and from A-B he is going 24km/hr and from B-A he is going 12km/hr.

Amortized is a fancy term that here essentially means average, so we want to find the average speed that the biker is traveling.

The actual distance that the person travels is not relevant because the distance from A to B is equivalent to the distance from B to A. For simplicity of the Math, lets say that the distance is 24 kilometers.

We can then say that at a rate of 24km/hr it would take 1 hour to get from A to B. We can also say that at a rate of 12hm/hr it would take 2 hours to get from B to A.

This means that in total it takes 3 hours to get from A to B back to A. In this time he has gone twice the distance (which we decided was 24). That means in total he traveled 48km.

If it took 3 hours to go 48km, that is (48/3)km/hr or just 16km/hr for the average (amortized) rate of speed.

You can see that the distance we decide upon is indeed irrelevant if you plug in x for the distance, and carry it through.