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The timescale for the accretion of bodies in the disk surrounding a young star depends upon a number of assumptions, but there are few observational constraints. In our own Solar System, measurements of meteoritic components can provide information about the inner regions of the nebula, but not the outer parts. Observations of the evolution of more massive protostellar systems (Herbig Ae/Be stars) imply that significant changes occur in the physical properties of their dust with time. The simplest explanation is that thermal annealing of the original, amorphous grains in the hot inner nebula slowly increases the fractional abundance of crystalline material over time. Crystalline dust is then transported outward, where it is incorporated into comets that serve as a long-term reservoir for dust disks, such as that surrounding Beta Pictoris. Here we show that when applied to our own Solar System, this process can explain observed variations in both the volatile and dusty components of comets, while also providing a natural indicator of a comet's mean formation age. Studies of comets with different dust contents can therefore be used to investigate the timescales of the early Solar System.