 For this example, we're going to be looking at two tasks that have been running continuously on machine A for a while. We've looked at the machine, we know that machine A spends about half of its time on the first task and the other half of its time on the second task. Now we have a second machine, machine B, that can run task number one in half as much time. So we'd like to see what kind of improvement we can get by running this workload on machine B instead of machine A. We'll begin by formalizing how machine A spends its time and we will look at how that relates to how much time it takes machine B to complete that same amount of work. So we know that machine A spends 50% of its time on task one, and it spends the other 50% of its time on task two. So together 50% of time, its time plus 50% of its time is 100% of its time. So it's spending all of its time working. This is pretty much what we'd expect. Now machine B is a little different. We know that machine B takes half as long to run the same amount of work that machine A did for task one. So we'll do this same amount of work in half as much time, but it takes just as long to run task two. So we won't see any change there. We'll still be spending this same amount of time on task two. Obviously if I add these up, we'll get 100 cent times time. So this tells me how much time we ran machine A for and found these two statistics. Now if I add these up, I've got 25% plus 50%, and I get 75% of this amount of time that it originally took machine A to run. So this is kind of nice because this is in terms of this is 100%. The fact that this says 75% times time means that this is going to be my final solution. It should be obvious that machine B is going to take only 3 fourths as much time as it took machine A to complete this same workload. But we can also put this into the relative performance equation. And in this case, we want to know how much faster machine B is than machine A. So I'm going to put machine B on the bottom and I'll put machine A on top. The T's will obviously cancel. This leaves me with 100% divided by 75%, which would be 4 thirds. So now I can say that machine B is 1.3 times faster than machine A. Alternatively, if I had left it as I had it before, it was telling me that machine B takes 3 fourths as much time to complete this task that as machine A did.