  We prove almost global existence for multiple speed quasilinear wave
equations with quadratic nonlinearities in three spatial dimensions. We prove
new results both for Minkowski space and also for nonlinear Dirichlet-wave
equations outside of star shaped obstacles. The results for Minkowski space
generalize a classical theorem of John and Klainerman. Our techniques only uses
the classical invariance of the wave operator under translations, spatial
rotations, and scaling. We exploit the $O(|x|^{-1})$ decay of solutions of the
wave equation as opposed to the more difficult $O(|t|^{-1})$ decay.
Accordingly, a key step in our approach is to prove a pointwise estimate of
solutions of the wave equations that gives $O(1/t)$ decay of solutions of the
inhomomogeneous linear wave equation based in terms of $O(1/|x|)$ estimates for
the forcing term.
