The rate of reaction between a solid and a gas can be substantially slowed when accompanied by an outward bulk flow of a nonreacting gas. Such gas may be generated by an independent decomposition reaction involving a second solid. The effect of the latter is analyzed theoretically. We have developed a useful approximate method of solution that makes the numerical solution of a second-order differential equation unnecessary. The approximate solution is especially useful in the analysis of multiparticle systems with a wide size distribution.