AAPL wrote:Veritas Prep
Brian takes a weekend trip to visit a friend. What is his average rate for the there-and-back trip?
1) Brian took the same route for both segments.
2) Brian averaged 80 mph for the first segment and 50 mph for the second segment.
$$? = {{{\rm{dist}}\,{\rm{there}} + {\rm{dist}}\,{\rm{back}}} \over {{\rm{time}}\,{\rm{there}} + {\rm{time}}\,{\rm{back}}}}\,\,\,\,\,\,\,\,\left[ {{{{\rm{miles}}} \over {\rm{h}}}} \right]$$
Each statement alone has a trivial bifurcation, hence they will be omitted.
Let´s use UNITS CONTROL, one of the most powerful tools covered in our course!
$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{dist}}\,{\rm{there}} = {\rm{dist}}\,{\rm{back}}\,\,{\rm{ = d}}\,{\rm{miles}} \hfill \cr
\,{\rm{time}}\,\,{\rm{there}} + {\rm{time}}\,{\rm{back}}\,\,\,{\rm{ = }}\,\,{\rm{d}}\,\,\,{\rm{miles}}\,\, \cdot \,\,\left( {{{1\,\,{\rm{h}}} \over {80\,\,{\rm{miles}}}}} \right)\,\,\,\,\, + \,\,\,\,\,\,\,{\rm{d}}\,\,\,{\rm{miles}}\,\, \cdot \,\,\left( {{{1\,\,{\rm{h}}} \over {50\,\,{\rm{miles}}}}} \right) \hfill \cr} \right.$$
$$? = {{2d} \over {\,\,d\left( {{1 \over {80}} + {1 \over {50}}} \right)\,\,}} = {2 \over {\,\,{1 \over {80}} + {1 \over {50}}\,\,}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{C}} \right)$$
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
