Hey, I can be useful! I do this for a living.
Is it an older Airport? It probably isn't gigabit (1000mbit speed), it's probably only fast (100mbit), so you plug directly in and are limited by the speed of the Airport (note that those speeds are megabit, not megabyte). It could also be that the ethernet chipset in the Airport isn't very good, I've read mixed reviews.
So, I would pick up a gigabit switch like
this one ($35 from Amazon)
And then wire it like this:
View attachment 9923
Edit: Of course, we could always replace the Airport, and you'll probably want to do that eventually since Apple dropped support for it earlier this year, but that's a whole can of worms I don't want to get in to. Lol. If you're fine with the WiFi on the rest of your devices, stick with the switch. If it ain't broke, don't fix it, right?
Edit 2: Looks like the Airport Extreme (The fat tall one) says it has Gigabit (1000), but will only do 400-500 in the real world, so it's operating at a pretty high loss%. The Airport Express (Short skinny one) only has fast (100). In either case, adding the switch in the middle will give you the same speed as if you were plugging directly into the modem.