jmc

First, $b$ must be positive since $b+\lceil b\rceil$ has a positive solution. Because $\lceil b\rceil$ must be an integer, $0.8$ must be the decimal component of $b$. Therefore, $b$ can be rewritten as $a+0.8$. $\lceil b\rceil$ must then equal $a+1$. The original equation is then as follows: $$\begin{array}{rl}b+\lceil b\rceil & =17.8\\ a+0.8+a+1& =17.8\\ 2a+1.8& =17.8\\ 2a& =16\\ a& =8\end{array}$$Therefore, $b=a+0.8=\boxed{8.8}$.