Seeing as to how this is a horror movie, it's pretty unlikely that someone won't fall and twist their ankle, or have to run back for their class ring or something. But barring disaster or plot device, yes, all four can cross in seventeen minutes.
First, Alexis and Burt dash hurriedly across in a heart-pounding two minutes.
Next brave 'ol Burt runs back, jumping at every sound, in an even more heart-poinding two minutes.
Then Dave lollygags across in ten minutes with Christine, as she shouts, "Come on! Hurry! Something's behind us!"
Now Alexis, who's thoroughly rested, bursts back across in a mere sixty seconds, as the theme music peaks.
Finally, she and Burt race back, again in two minutes, completing the relay in exactly seventeen minutes as the music reaches its terrifying crescendo.
Of course, by this time Dave and Christine have been eaten. But Alexis and Burt will live happily ever after. Or will they? (Da da da dum...)