dynamo wrote:

Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?

A. 1/8

B. 2/15

C. 3/15

D. 1/4

E. 3/8

\({\text{2}}\,{\text{miles}}\,\,\,\,({\text{go}}\,\,{\text{and}}\,\,{\text{back}})\)

\({V_{{\text{run}}}} = \frac{{10\,\,{\text{miles}}}}{{1\,\,{\text{h}}}}\,\,\,\,\,\,;\,\,\,\,\,{V_{{\text{swim}}}} = \frac{{6\,\,{\text{miles}}}}{{1\,\,{\text{h}}}}\)

\(?\,\,:\,\,\,\,\frac{{{\text{total}}\,\,{\text{miles}}}}{{{\text{total}}\,\,{\text{minutes}}}} = \frac{{4\,\,{\text{miles}}}}{{?{\,_{{\text{temporary}}\,\,{\text{focus}}}}}}\)

Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our method!

\(\left. \begin{gathered}

{\text{Run}}:\,\,\,2\,{\text{miles}}\,\,\left( {\frac{{1\,\,{\text{h}}}}{{10\,\,{\text{miles}}}}\,\,\begin{array}{*{20}{c}}

\nearrow \\

\nearrow

\end{array}} \right)\,\,\left( {\frac{{60\,\,{\text{minutes}}}}{{1\,\,h}}\,\,\begin{array}{*{20}{c}}

\nearrow \\

\nearrow

\end{array}} \right)\,\,\, = \,\,12\,\,{\text{minutes}} \hfill \\

{\text{Swim}}:\,\,\,2\,{\text{miles}}\,\,\left( {\frac{{1\,\,{\text{h}}}}{{6\,\,{\text{miles}}}}\,\,\begin{array}{*{20}{c}}

\nearrow \\

\nearrow

\end{array}} \right)\,\,\left( {\frac{{60\,\,{\text{minutes}}}}{{1\,\,h}}\,\,\begin{array}{*{20}{c}}

\nearrow \\

\nearrow

\end{array}} \right)\,\,\, = \,\,20\,\,{\text{minutes}} \hfill \\

\end{gathered} \right\}\,\,\,\, \Rightarrow \,\,\,\,?{\,_{{\text{temporary}}\,\,{\text{focus}}}}\,\, = \,\,\,32\,\,{\text{minutes}}\)

\({\text{? = }}\frac{{\text{4}}}{{32}} = \frac{1}{8}\)

Obs.: arrows indicate licit converters.

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

_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)

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