He looks up and down the smoke-filled corridor, trying not to think of Gallifrey. Stop ditherin' an' get your mind out of the past. Rescue will be easy enough: just run to the far end of the doomed Ikridu ship, gather up an unconscious human, and run to the safety of the TARDIS. Easy as falling off a log. All he has to do is decide which of his companions will be left to die: Rose or Jack.
At first it seems that -- once again -- disaster has been averted by Time Lord genius and human ingenuity. Captain Trelk of Ikrid's Valour is interrogating his three alien 'stowaways' when Jack notices the slight irregularity in the thrum of the ship's engines. It takes only a few minutes for the Doctor to find the flaws in the power conduits; a few minutes longer to decide that the deterioration is unstoppable. Even a complete engine shutdown will not prevent a massive explosion.
"But we can delay it," he tells the gobsmacked captain cheerfully. "Me an' Jack can rig up a few hypothermic power dampers. Temporary reversal of polarity to the neutron flow, an' that'll buy enough time for all the lifepods to get clear of the ship."
Rose organises the evacuation with a brisk authority that reminds him of Tegan in full air-hostess mode. "Sorry, you can't go back to your cabin to get your souvenirs from Delta Omega IV. No, I don't know how much they cost, and I don't care. Move along."
The jiggery-pokery is completed just as Captain Trelk boards the last lifepod. It takes some blunt words to persuade him to leave. "You're of no use here, so shove off. We've got work to do." The dampers need to be positioned at equidistant points around the ship, and with the clock ticking, the job has to be done quickly. Like the rest of his species, Trelk moves with the speed of an arthritic snail. He takes one mournful last look at his ship and closes the hatch of the lifepod behind him.
If Ikrid's Valour had been a larger vessel, setting out the dampers in time would be an impossible task. The TARDIS trio divide the sectors of the ship between them, sprinting along the deserted corridors. As soon as his jury-rigged control device shows that all of the dampers are in place, the Doctor keys in the activation sequence. The blue indicator lights begin to blink: Flash-FLASH, flash-FLASH, flash-FLASH. The simple synchopated pattern reminds him of a human heartbeat; a rhythm he finds oddly comforting these days.
Time to get back to the TARDIS and rendezvous with his companions. The perpetual clock in his head tells him they have enough time, plus a safety margin. Still, he'll feel better once they're in the Vortex. He's scarcely started moving when he hears a muted bang, followed by the shrill whine of an alarm, then the loud hiss of the fire suppressant system. He ignores the grey mist that fill the corridor -- a mostly harmless combination of smoke and fire suppressant chemicals. Then he catches a faint whiff of a sweet odour, something like licorice.
He spits out a curse. The noise must've been a breach in the coolant pipes. That licorice scent is alpha-dicadmolene -- a gas deadly to humans -- and the efficient ventilation system is carrying it all over the ship.
He runs through the calculations once again: his companions' last known locations; how fast they can run; when the poison-tainted air will reach them; and how soon they will become dizzy, then unconscious. The numbers refuse to change. He has only enough time to locate one of his companions, carry the senseless human back to the TARDIS, and administer the antidote. Even if the damned ship takes much longer than it ought to explode, the Doctor's other companion will be dead before he can come to the rescue. It is impossible to save them both.
He slams a fist against the nearest bulkhead. "I'll find some other way. I'm the Doctor. I don't accept 'impossible'. I do the impossible every bloody day an' twice on Sundays." He curses fate, the Ikridu, the shipyard that built this deathtrap, the crooked inspectors that let it launch, and the witless crew who didn't notice the flaw in their own engines until a stranger pointed it out.
Use the TARDIS to get from one end of the ship to the other? No. As soon as he dematerialises, the fluctuation of energies will kill the damper circuit, and Ikrid's Valour will explode. Stop the coolant leak? Shut down the ventilators? Not enough time. There are emergency airmasks all over the ship, but they're made to fit the wide ursine faces of the Ikridu; they won't seal tightly enough to protect humans from toxic fumes. He runs through a dozen more ideas, discarding each one. Time elapsed since the coolant leak: 12.4 seconds.
He stares at the roiling grey clouds filling the corridor, and Gallifrey looms in his mind. He hasn't been faced with such a painful choice since the War. In some ways, ending the Time War was easier. It was total destruction -- he hadn't been forced to decide who would live and who would die. He hadn't worried about making explanations to anguished survivors. Hell, he hadn't expected to survive himself.
Images flit though his mind with painful clarity: Rose, pink tongue caught between her teeth as she concentrates on picking the lock of a prison cell; laughing in delight at the giant singing butterflies of Mela'ai'tsao; facing Gelth and Slitheen and gas-mask zombies with defiant courage. Jack, hunched beneath the TARDIS console, his clever fingers coaxing a wire into place; stepping between Rose and a Xoric warrior, his only weapons a fierce glare and a non-functioning blaster; leaping, naked and whooping like a maniac, from a second-floor balcony into the Grand Canal on Nuova Venezia. He can see them, running beside him from (or towards) danger; joyously shedding doubts and clothing, on the day the three of them sealed their partnership; sprawled in bed, sweaty and loose-limbed with contented exhaustion.
He rages at the Universe: I can't do this! Might as well give me a knife and tell me to cut out one of my hearts. No matter which companion he chooses, he's going to lose them both; one to death, and the other to grief and anger. The survivor won't forgive him, any more than he'll forgive himself. Get on with it! Time elapsed since the coolant leak: 14.9 seconds. He turns towards the aft of the ship and begins to run.