No, you're misunderstanding. You are both swimming in the same direction: them in front swimming away, and you behind swimming toward them. There is a consistent 10m separation because you're both swimming at the same pace. When a problem develops, you have to catch them. You increase your speed, but being unaware of the issue, they continue at their same pace. The separation is not reduced by your new speed of 10m/min, but by the *difference* in your speeds. If the original speeds were 8m/min, it will take 5 minutes to catch them. In this statement, you are clearly assuming they are stationary:Your scenario puts the maximum buddy separation at a far greater distance than the 10 meters that I stated it to be. You're changing the narrative.
10 meters is 5 diver lengths. Or a nice sized living room. If that takes you more than a minute at a regular pace there are problems here.