John has to hammer 100 railroad spikes for a new line his

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John has to hammer 100 railroad spikes for a new line his company is building. Working at a constant rate, he can hammer 8 spikes per hour. When he is halfway done, his coworker Paul begins working at the same constant rate. Compared to John completing all the work alone, how many hours are saved with Paul's help?

A. 5/2
B. 23/8
C. 25/8
D. 17/4
E. 25/4

\[?\,\,\,:\,\,\,{\text{hours}}\,{\text{saved}}\,\,{\text{ = }}\,\,{\text{Time}}\,\left( {{\text{John}}\,,\,50\,\,{\text{spikes}}} \right) - {\text{Time}}\left( {{\text{John}} \cup {\text{Paul}}\,,\,50\,\,{\text{spikes}}} \right)\]
\[{\text{Time}}\,\left( {{\text{John}}\,,\,50\,\,{\text{spikes}}} \right)\,\, = \,\,50\,\,spikes\,\,\left( {\frac{{1\,\,{\text{h}}}}{{8\,\,{\text{spikes}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \frac{{25}}{4}\,\,{\text{h}}\]
\[{\text{Time}}\,\left( {{\text{John}} \cup {\text{Paul}}\,,\,50\,\,{\text{spikes}}} \right)\,\, = \,\,50\,\,spikes\,\,\left( {\frac{{1\,\,{\text{h}}}}{{16\,\,{\text{spikes}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \frac{{25}}{8}\,\,{\text{h}}\]
Obs.: arrows indicate licit converters.
\[{\text{?}}\,\,{\text{ = }}\,\,\frac{{25 \cdot \boxed2}}{{4 \cdot \boxed2}} - \frac{{25}}{8} = \frac{{25}}{8}\,\,\,\left[ {\text{h}} \right]\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.