This will only be my way of looking at this.
I have played some of the earlier Starter Set adventures, but not the Burnt Beast episode.
However, clearly you need to offer/suggest enough opportunities for the Player-heroes to achieve the three Successes, before moving things along.
After each attempt, you might add a line indicating how much time has passed.
e,g while Rory Brandybuck wanders around from tree to tree examining the ground (his Scan roll?), the LM could add commentary about how, "... for the time of year the leaves on the trees are showing signs of poor growth. In fact, while Rory is prodding around, a half hour passes, which is enough time for the breeze to freshen and his hat is sent rolling off into some long grass next to a particularly dense patch of gorse bushes. (change tone of narration) The gorse bushes are so dense it would be very difficult to see much into them when the sun sets in a few more hours..."
And back to LM prompt: "What are the other hobbits doing while Rory is busy? Time is passing, the sun will set sometime today, making things more difficult, apart from the awful fear that you might miss out on the Late Tea back at the inn!"
(LM mutters behind Loremasters Screen - four o'clock, so three hour till dusk)
Or something like this.