Meteorite chronometry based on the Hf-182-W-182 system can provide powerful constraints on the timing of planetary accretion and differentiation(1-4), although the full potential of this method has yet to be realized. For example, no measurements have been made on the silicate-rich portions of planets and planetesimals other than the Earth and Moon. Here we report tungsten isotope compositions for two eucrites, thought to be derived from asteroid 4 Vesta, and from eight other basaltic achondritic meteorites that are widely considered to be from Mars. The eucrites, which are among the oldest differentiated meteorites, yield exceedingly radiogenic tungsten, indicating rapid accretion, differentiation and core formation on Vesta within the first 5-15 Myr of Solar System history, whereas the range of radiogenic tungsten measurements on the martian meteorites points towards tungsten depletion via melting and core formation within the first 30 Myr of the Solar System. The survival of tungsten isotope heterogeneity in the martian upper mantle implies that no giant impacts or large-scale convective mixing took place since this time, These results contrast with those obtained for the Earth-Moon system(2,3) for which accretion and core formation related to giant impacts appears to have continued for at least an additional 20 Myr.