BTGmoderatorDC wrote:On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?

(1) The machine began filling the order at 9:30 a.m.
(2) The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m.
Source: Official Guide

Although a careful reading guarantees choosing the right answer without ANY need of writing,
let´s use this easy problem to practice UNITS CONTROL, one of our method´s most powerful tools!
\[?\,\,:\,\,{\text{time}}\,\,{\text{it}}\,\,{\text{finished}}\,\,{\text{the}}\,\,{\text{order}}\]
\[\left( 1 \right)\,\,{\text{If}}\,\,{\text{it}}\,\,\left\{ \begin{gathered}
{\text{takes}}\,\,30\min \,\,\, \Rightarrow \,\,\,? = 10\,\,{\text{a}}{\text{.m}}{\text{.}} \hfill \\
{\text{takes}}\,\,90\min \,\,\, \Rightarrow \,\,\,? = 11\,\,{\text{a}}{\text{.m}}{\text{.}} \hfill \\
\end{gathered} \right.\]\[\left( 2 \right)\,\,\, \Rightarrow \,\,\frac{{\,\,\left( {\frac{5}{6} - \frac{1}{2} = } \right)\,\,\,\frac{1}{3}\,\,{\text{order}}\,\,}}{{40\,\,\min }}\]
\[\frac{1}{2}\,\,{\text{order}}\,\,\left( {\frac{{40\,\,\min }}{{\frac{1}{3}\,\,{\text{order}}}}} \right) = 60\,\,\min \,\,\,\left( {{\text{for}}\,\,{\text{half - order}}} \right)\,\,\]
\[?\,\, = \,\,10{\text{h}}30\min + 60\min \,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\]

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

Regards,
fskilnik.