Brian takes a weekend trip to visit a friend. What is his average rate

I am not sure if the question is poorly worded. How can we interpret segments to the actual journey to a place and from a place. There couple be multiple segments within the same route...

Could you or somebody please elaborate why in the equation we just replaced D? I thought I wouldn't be able to solve it since I did not have a value for D (but did come up with the same equation).

I marked answer as E as I assumed that weekend trip includes some stay at the trip place and we do not know stay time at place. Am I wrong to assume it as it is not mentioned in question or just use time and distance and stay time can be ignored for calculation.

\(? = {{{\rm{dist}}\,{\rm{there}} + {\rm{dist}}\,{\rm{back}}} \over {{\rm{time}}\,{\rm{there}} + {\rm{time}}\,{\rm{back}}}}\,\,\,\,\,\,\,\,\left[ {{{{\rm{miles}}} \over {\rm{h}}}} \right]\)

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.

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