  We introduce a straightforward method to analyze the blow-up of systems of
ordinary differential inequalities, and apply it to study the blow- up of
solutions to a weakly coupled system of semilinear heat equations. We prove
that the solution blows up in a finite time under the subcritical condition.
Moreover, we give estimates of lifespan of the solution and lower estimates of
the blow-up rate for a localized average of each component.
