Answer
See below.
Work Step by Step
Let $x$ be Bruce's "speed", $y$ be Bryce's and $z$ be Marty's. Then our equations are: $(x+y)\frac{4}{3}=1$, $(z+y)\frac{8}{5}=1$, $(x+z)\frac{8}{3}=1$.
So $(x+y)=\frac{3}{4}$, $(z+y)=\frac{5}{8}$, $(x+z)=\frac{3}{8}$.
Thus $x=0.75-y$, so $(0.75-y)+z=0.375$, so $z-y=-0.375$, thus $z=-0.375+y$.
So $(-0.375+y)+y=0.625$, thus $y=0.5$, so $z=0.125$ and $x=0.25$
Thus Bruce needs $\frac{1}{0.25}=4$ hours, Bryce needs $\frac{1}{0.5}=2$ hours and Marty needs $\frac{1}{0.125}=8$ hours
