#### Answer

9$\frac{5}{8}$ in

#### Work Step by Step

Let the two lenghs given are 6$\frac{3}{4}$ in and 2$\frac{7}{8}$ in
Total length of the shaft = 6$\frac{3}{4}$ in + 2$\frac{7}{8}$ in
=$\frac{27}{4}$ +$\frac{23}{8}$
=$\frac{27}{4}\times$ $\frac{2}{2}$ +$\frac{23}{8}$
= $\frac{54}{8}$ +$\frac{23}{8}$
=$\frac{77}{8}$
=9$\frac{5}{8}$ in