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This article presents a measurement of the top quark mass using the CDF II detector at Fermilab. Colliding beams of protons and antiprotons at Fermilab’s Tevatron (√s = 1.96 TeV) produce top/antitop pairs, which decay to W+W-bb̅; events are selected where one W decays to hadrons and the other W decays to either ℯ or μ plus a neutrino. The data sample corresponds to an integrated luminosity of approximately 318 pb-1. A total of 165 tt̅ events are separated into four sub-samples based on jet transverse energy thresholds and the number of b jets identified by reconstructing a displaced vertex. In each event, the reconstructed top quark invariant mass is determined by minimizing a χ2 for the overconstrained kinematic system. At the same time, the mass of the hadronically decaying W boson is measured in the same event sample. The observed W boson mass provides an in situ improvement in the determination of the hadronic jet energy scale. A simultaneous likelihood fit of the reconstructed top quark masses and the W boson invariant masses in the data sample to distributions from simulated signal and background events gives a top quark mass of 173.5-3.8+3.9 GeV=c2.