= Solution
Let $L_J$ be <Jupiter>'s current total emitted luminosity. Under the stipulated split, its intrinsic luminosity after removal of sunlight is approximately $L_J/2$. If the accessible energy reservoir down to $T_{\rm cold}$ is $E_J$, the constant-luminosity estimate gives $\tau\simeq E_J/(L_J/2)$.
Assume the more massive giant has approximately the same radius as <Jupiter>, a comparable structure factor, and an accessible cooling reservoir scaling as $GM^2/R$, as in the <Kelvin-Helmholtz cooling time>. Assume also that the final cold state contributes negligibly to that reservoir and that the giant radiates at the constant stipulated luminosity $L_J$. Then
$$
E_{10}\simeq100E_J,\qquad
\tau_{10}\simeq\frac{100E_J}{L_J}.
$$
Therefore
$$
\boxed{\tau_{10}\simeq50\tau.}
$$
This is a characteristic scaling under the stated assumptions, not a detailed evolutionary age. A different mass-radius relation, a different accessible internal-energy fraction, or time-dependent luminosity changes the result; the mass and luminosity alone do not uniquely determine a cooling time.
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