He was worn, not exhausted. Exhausted would mean if he laid down, getting up soon after would not be possible. But he wasn't going to argue the details. Too exhausted.

He looked from the shower area to the tub and decided an actual bath might help more than the new shower. "Join me?" he requested, turning the faucet on and letting the tub fill as he worked his clothes off. He had to admit, sex might help him relax more, but for now, the bath would suffice.