The average lifetime of B hadrons produced in hadronic Z0 decays has been measured with the DELPHI detector at LEP. The measurement is based on the analysis of the impact parameter distribution of high p(t) muons and hadrons. The resulting mean B lifetimes are tau(B) = (1.30 +/- 0.10 +/- 0.08) ps and tau(B) = (1.27 +/- 0.04 +/- 0.12) ps respectively, giving a combined value of tau(B) = (1.28 +/- 0.10) ps. The hadronic sample was also used to measure the partial Z0 width GAMMA(bbBAR)/GAMMA(h) and gave a value of 0.222(-0.031)+0.033 +/- 0.017.