In this work, we model the collisional evolution of the Jupiter Trojans and determine under which conditions the Eurybates-Queta system survives. We show that the collisional strength of the Jupiter Trojans and the age of the Eurybates family and by extension Queta are correlated. The collisional grinding of the Jupiter Trojan population over 4.5Gy results in a size-frequency distribution (SFD) that remains largely unaltered at large sizes (>10km) but is depleted at small sizes (10m to 1km). This results in a turnover in the SFD, the location of which depends on the collisional strength of the material. It is to be expected that the Trojan SFD bends between 1 and 10km. Based on the SFD of the Eurybates family, we find that the family was likely the result of a catastrophic impact onto a 100km rubble pile target. This corresponds to objects with a rather low collisional strength (10 times weaker than that of basaltic material studied in Benz & Asphaug). Assuming this weak strength, and an initial cumulative slope of the size-frequency distribution of 2.1 between diameters of 2m and 100km when the Trojans were captured, the existence of Queta, the satellite of Eurybates, implies an upper limit for the family age of 3.7Gy. Alternatively, we demonstrate that an unconventional collisional strength with a minimum at 20m is a plausible candidate to ensure the survival of Queta over the age of the solar system. Finally, we show how different collisional histories change the expected number of craters on the targets of the Lucy mission and that Lucy will be able to differentiate between them.