goodyear2013 wrote:

Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24

B. 36

C. 48

D. 50

E. 64

\(?\,\,\,:\,\,\,\# \,\,\,{\text{minutes}}\,\,X\,\,{\text{fills}}\,\,{\text{container}}\)

Excellent opportunity to use

UNITS CONTROL, one of the most powerful tools of our method!

\(X\,\,:\,\,\,\,\frac{{x\,\,{\text{gallons}}}}{{1\,\,{\text{minute}}}}\,\,\,\,\,\left( {{\text{filling}}} \right)\)

\(Y\,\,:\,\,\,\,\frac{{y\,\,{\text{gallons}}}}{{1\,\,{\text{minute}}}}\,\,\,\,\,\left( {{\text{draining}}} \right)\,\,\)

The filling TIME ratio 4:1 (for any given volume) of water is

inversely proportional to the filling VOLUME ratio (for any given time), hence:

\({\text{Relative}}\,\,{\text{volume}}\,\,\left( {{\text{filling}}} \right)\,\,{\text{rate}}\,\,\,:\,\,\,\,\frac{1}{4} = \frac{{\frac{{\left( {x - y} \right)\,\,{\text{gallons}}}}{{1\,\,{\text{minute}}}}}}{{\frac{{x\,\,{\text{gallons}}}}{{1\,\,{\text{minute}}}}}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\, \ldots \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\frac{x}{y} = \frac{4}{3}\,\,\,\)

\(y = 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}

\,\,x = 4\, \hfill \\

48\,\,{\text{minutes}}\,\,\,\left( {\frac{{3\,\,{\text{gallons}}}}{{1\,\,{\text{minute}}}}} \right)\,\,\, = \,\,\,48 \cdot 3\,\,{\text{gallons}}\,\,\, = \,\,\,{\text{Volume}}\,\,{\text{container}} \hfill \\

\end{gathered} \right.\)

\({\text{?}}\,\,\,{\text{ = }}\,\,\,48 \cdot 3\,\,{\text{gallons}}\,\,\left( {\frac{{1\,\,{\text{minute}}}}{{4\,\,{\text{gallons}}}}} \right)\,\,\,\, = \,\,\,\,36\,\,{\text{minutes}}\)

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

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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