Problem Solving

Official Guide

When traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

A. 2/3
B. 3/4
C. 4/5
D. 4/3
E. 3/2

OA D

AAPL wrote: When traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

A. 2/3
B. 3/4
C. 4/5
D. 4/3
E. 3/2

\[\frac{{k\,\,\,miles}}{{1\,\,\,{\text{gallon}}}}\,\,\, = \,\,\,\,k\,\,\,\frac{{miles}}{{{\text{gallon}}}}\]

\[? = k\]

\[\frac{{32\,\,{\text{miles}}}}{{1\,\,\,{\text{h}}}}\,\,\,\,\, \to \,\,\,\,\,\,\frac{{{\text{24}}\,\,\,{\text{gallons}}}}{{1\,\,\,{\text{h}}}}\]

\[\left( {\frac{{32\,\,{\text{miles}}}}{{1\,\,\,{\text{h}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\left( {\frac{{1\,\,{\text{h}}}}{{{\text{24}}\,\,\,{\text{gallons}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\frac{{32 \div \boxed8}}{{24 \div \boxed8}} = \frac{4}{3}\,\,\,\,\,\,\,\,\,\left[ {\frac{{{\text{miles}}}}{{{\text{gallon}}}}} \right]\]

Obs.: arrows indicate licit converters. (This is a nice example of UNITS CONTROL, one of the most powerful tools of our method.)

The above follows the notations and rationale taught in the GMATH method.