Tropical forests have a high diversity of tree species which have very low densities and vary across time in their seasons of peak fruiting and maturation rates. As evidence of the ability of primates to track or anticipate changes in fruit production at individual trees, researchers have used the increased speed of primate groups toward more rewarding food patches. We analyzed the speed of approach to natural trees of wild capuchin monkeys under the effect of scramble competition, after excluding any plausible visual, olfactory and auditory cues. We conducted all-day group follows of three habituated capuchin groups at Iguazú National Park, Argentina, collecting data on ranging behavior and patterns of visits to fruit trees in relation with their location and fruit availability. Travel speed varied according to the expected reward at a feeding tree, increasing as rewards increased from low values, but decreasing again at very high values. Also, travel speed varied with time of day, decreasing from the time of first activity as the monkeys became less hungry, and increasing again toward late afternoon. Measures of unripe fruit cover did not explain variation in travel speed at any distance from a focal tree. Our data imply that, after excluding sensory cues, capuchins appear to anticipate time-varying ripe fruit quantity of natural resources, suggesting that they use memory of tree location and anticipation of fruit maturation. We also confirm that speed is a good measure about expectations of resources, as has been shown in previous studies.