Ok, first I am not an math major but when I thought about the problem I thought about my own sons' washing my car. The older one can wash it in 6 minutes and the younger in 8 minutes. They both start washing the car at the same time. Older son finishes his side in 3 minutes and younger in 4 minutes--are you suggesting that the boy who finishes his side first would begin to help wash his brother's side so they would finish in 3 and a half minutes instead of four? The car is not clean until both sides are done. Four minutes.
Exactly. These sorts of problems have a built-in assumption that the work can be divided with perfect efficiency (which is generally false in the real world, as others have noted). So the boy who does his half in 3 minutes starts working on what's left over on the other half at the same rate, and the slower boy ends up doing less than half.