= Solution
With no delayed <neutrons>, set $\beta=0$ and omit the precursor equation. The source-free model reduces to $\dot n=(\rho/\Lambda)n$, giving
$$
\boxed{T_{\rm prompt\ only}=\frac\Lambda\rho=0.500\ \mathrm s.}
$$
The delayed-<neutron> model's dominant e-folding time is about $121$ times larger. This comparison illustrates why a small <delayed neutron fraction> strongly alters the kinetics. It is a comparison of the supplied idealized models at the same imposed positive <reactivity>, not a control prescription or a claim that every transient has the same timescale.
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