38 hours is an estimate, of course. Let's assume you have the 230 trade fodder Pokémon on Platinum all ready to be traded one by one to Pearl. A Pokémon trade takes... what, 4 minutes from start to finish, saving included? That's 230 x 4 minutes = 920 minutes = roughly 15 hours.
To that 15 hours, add to the fact that every six Pokémon, you're going to have to go back to the PC and swap out the ones you've just traded for and swap in the next ones to go. Let's say, arbitrarily, that each one of those switches takes 6 minutes. 230 Pokémon / 6 = 38.3 (repeating, of course) x 6 minutes = 230 minutes = just under another 4 hours.
So the rough total is about 19 hours total. Even better than the 38. You could be done by dinnertime tonight/tomorrow.