BTGmoderatorDC wrote:A certain liquid passes through a drain at a rate of w/20 gallons every x seconds. At that rate, how many minutes will it take y gallons to pass through the drain?

A. y/(1200xy)
B. 20xy/w
C. xy/(3w)
D. w/(3xy)
E. 3y/(wx)

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

\[\frac{{\,\,\frac{w}{{20}}\,\,}}{x}\,\,\,\frac{{{\text{gallons}}}}{{\text{s}}}\,\,\, = \,\,\,\frac{w}{{20\,\,x}}\,\,\,\frac{{{\text{gallons}}}}{{\text{s}}}\]
\[?\,\,\,\min \,\,\, \leftrightarrow \,\,\,y\,\,\,{\text{gallons}}\,\]

\[?\,\,\, = \,\,\,y\,\,{\text{gallons}}\,\,\,\left( {\frac{{\,20\,\,x\,\,{\text{s}}\,}}{{w\,\,{\text{gallons}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\,\left( {\frac{{\,1\,\,\min \,}}{{60\,\,{\text{s}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{20\,\,xy}}{{60\,\,w}}\,\,\, = \,\,\,\frac{{xy}}{{\,3w\,}}\,\,\,\,\,\,\,\,\left[ {\min } \right]\]
Obs.: arrows indicate licit converters.


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

Regards,
Fabio.