= Solution
Adopt the approximate <mass-luminosity relation> $L/L_\odot\simeq(M/M_\odot)^3$ and equal available fuel fractions. The <main-sequence lifetime> then scales as $M/L$, giving
$$
\boxed{t_1\simeq1.54\times10^8\,\mathrm{yr},\qquad t_2\simeq6.16\times10^8\,\mathrm{yr}.}
$$
Using an exponent $3.5$ instead gives about $5.4\times10^7$ and $3.1\times10^8$ years; these are model-dependent estimates. At $r=3r_s=6GM/c^2$ the <Newtonian gravitational potential energy> released from infinity is $GMm/r=mc^2/6$. Half remains as <kinetic energy> in a circular <orbit>, so the radiatable <binding energy> is $GMm/(2r)$:
$$
\boxed{\eta_{\rm Newtonian}=\frac1{12}\simeq8.3\%.}
$$
Using the whole <potential energy> loss would give $1/6$, which does not subtract the final <kinetic energy>. A fully relativistic calculation for a nonrotating <black hole> gives $1-\sqrt{8/9}\simeq5.7\%$. When the surviving star exhausts <hydrogen burning>, it expands off the <main sequence> and can fill its <Roche lobe>. <Binary mass transfer> to the <black hole> can form an <accretion disk> and an <X-ray binary>; unstable <binary mass transfer> may instead produce a <common envelope>. This is conditional on the <binary star> remaining bound after the first remnant forms. The supplied <black hole> endpoint is an assumption, not a universal outcome for an isolated $8M_\odot$ star.
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