Upon reaching Whitebridge, we see Moiraine appear to reverse her initial decision, abandoning the pursuit of the coinless lads (Mat and Rand) in favor of the one she can sense with the coin (Perrin).
First, I must find the one I can be sure of finding, and at present he is somewhere to the north of us. I do not think the other two went with the boat in any case." A small, satisfied smile touched her lips. "They were in this room, perhaps a day ago, no more than two. Afraid, but they left alive. The trace would not have lasted without that strong emotion."
... "If they're only a day or two ahead, why don't we go after them first?"
"I know they were here," Moiraine said in that insufferably calm voice, "but beyond that I cannot say if they went east or north or south. I trust they are smart enough to have gone east, toward Caemlyn, but I do not know, and lacking their tokens, I will not know where they are until I am perhaps within half a mile. In two days, they could have gone twenty miles, or forty, in any direction, if fear urged them, and they were certainly afraid when they left here."
Moiraine and Nynaeve, The Eye of the World, p. 353-354
A few chapters ago, following the fracturing of the band at Shadar Logoth, Moiraine was intent on following the boys missing their coins. Why the sudden reversal of decisions? Despite constant knowledge of the general location of Perrin, Moiraine had no way to reach him. Part of the original plan for coming through Shadar Logoth was to have the party build rafts and cross the Arinelle while she held the enemies at bay. Doing so to track Perrin down would have been a waste of time; time that could be better served trying to track down Mat and Rand.
Now that Moiraine can cross the Arinelle with ease, she chooses to adjust the plan to find the one she knows without a doubt she can find. She has confirmation that the other two were still alive up until a day or two ago. Without their coins, Moiraine can only guess the direction they bolted in, and any step she takes could take her further away from the two. Constant evaluation of the situation allows Moiraine to adjust the course at the most influential moments.