This isn't necessarily a difficult question, but it's something I'm trying to set straight.
The task I have in mind is mowing my lawn. Let's say I have a 16" lawnmower. I decide I'd rather have a wider one, so I get a 20" lawnmower to replace it. So the new lawnmower is 25% wider than the old one. How much faster is it? You would intuitively guess it's also 25% faster, but I've been turning it over in my head and now say it would be only 20% faster.
Is this correct, or is it simply a matter of interpretation or point-of-view? In other words, could both be correct depending on how you look at it? I'm wondering if there is a formal definition, i.e. do we say 4/5 or 5/4?
My understanding is that you are assuming that the length of the new lawnmower is the same as the old one and that the new lawn mower is pushed at the same speed as the old one. Consequently, it mows $5/4$ as much area in the same amount of time as the old one. Since your lawn does not change area, this means the new lawnmower can be used to mow the lawn in $4/5$ the amount of time as the old one. Therefore, the amount of time needed to mow the lawn decreases by $20\%$ and the area that can be mowed in a given amount of time increases by $25\%$. Since the rate at which we can mow the lawn is the amount of area mowed divided by the time it takes to mow it, switching to the wider lawn mover increases the rate at which we mow the lawn by $25\%$.