BTGmoderatorDC wrote:How many hours did it take Dale to drive from A-town to B-town?
(1) If Dale's average speed for the trip had been three times as fast, the trip would have taken 2 hours.
(2) The distance from A-town to B-town is 100 miles.
Source: Magoosh
Excellent opportunity to practice UNITS CONTROL and BIFURCATION, two of our most powerful tools!
\[? = {T_{\,A\, \to \,B}}\,\,\,\left[ {\text{h}} \right]\,\,\,\,\mathop = \limits^{{\text{UNITS}}\,\,\,{\text{CONTROL}}\,\,\left( * \right)} \,\,\,\,\,\,\boxed{\frac{{d\,\,\,{\text{miles}}}}{{V\,\,\frac{{{\text{miles}}}}{{\text{h}}}}} = ?}\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,\,\frac{{{\text{miles}}}}{{\,\,\,\,\frac{{{\text{miles}}}}{{\text{h}}}\,\,\,}} = {\text{h}}\,} \right]\]
\[\left( 1 \right)\,\,\,2\,{\text{h}}\,\,\left( {\frac{{3V\,\,{\text{miles}}}}{{1\,\,\,{\text{h}}}}} \right)\,\,\, = \,\,\,6V\,\,{\text{ = }}\,\,\,{\text{d }}\,\,\,\left[ {{\text{miles}}} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\, = \frac{{6V}}{V} = 6\,\,\,\left[ {\text{h}} \right]\,\,\]
\[\left( 2 \right)\,\,\,d = 100\,\,{\text{miles}}\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\,{\text{V = }}\,\,{\text{100}}\,\,{\text{mph}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{1}}\,\, \hfill \\
\,{\text{Take}}\,\,\,{\text{V = }}\,\,5{\text{0}}\,\,{\text{mph}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,2\,\, \ne 1\,\,\, \hfill \\
\end{gathered} \right.\,\,\,\left[ {\text{h}} \right]\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
