They find the answer in the Jurassic Period, which is where the time contour that hijacked them ends. The crew and passengers of the other flight are under some hypnotic influence, all that is except for a Professor Hayter, a university scientist specializing in hypnotism who was unaffected. He thinks that the plane was hijacked by the Soviets and that they are behind the iron curtain.
The sight of a crashed spaceship, a citadel, and a grotesque-looking Oriental magician named Kalid, leads the travellers to believe there's more to their predicament.
Nyssa plays a larger role by acting as a medium for some aliens divided into good and evil halves, and there's a kind of sixth sense about her, which may come from her being from Traken. And at least Tegan finally gets to be a stewardess, having worn her uniform all throughout the season.
I can't tell more without spoiling the rest. Paleontology seems to be a weak case in Doctor Who (q.v. The Silurians, The Sea Devils). 140 million years ago is indeed the close of the Jurassic Period, but then the Doctor says they must be near the Pleistocene Era. Two goofs: he must have meant the Cretaceous Era, and second, it should be the Pleistocene Epoch, which wouldn't occur for another 138 million years after.
Some credit should be given to British Airways giving producer John Nathan-Turner permission to feature the Concorde and airport authorities giving him the go-ahead to film at Heathrow.
Occasionally, the series has some stories that don't cut the mustard, and sadly, Timeflight is one of them. The regulars come out good as usual, with worthy performances from Richard Easton (Stapley) and Nigel Stock (Hayter). The main problem, though, is the concept of two Concordes being hijacked to the end of the Jurassic Period and the bad story idea and execution.