Stiv wrote:
The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)
A. \((\frac{20}{5280})(\frac{60^2}{0.5})\)
B. \((\frac{20}{5280})(\frac{60}{0.5})\)
C. \((\frac{20}{5280})(\frac{0.5}{60^2})\)
D. \(\frac{(20)(5280)}{(60^2)(0.5)}\)
E. \(\frac{(20)(5280)}{(60)(0.5)}\)
\(1\,\,{\rm{mile}}\,\,\, \leftrightarrow \,\,\,5280\,\,{\rm{feet}}\)
\(V\left( {{\rm{speed}}} \right) = {{\,20\,\,{\rm{feet }}} \over {0.5\,\,{\rm{s}}}}\,\, = \,\,\,?\,\,{\rm{mph}}\,\,\,\,\,\)
Perfect opportunity to use
UNITS CONTROL, one of the most powerful tools of our course!
\(?\,\,\, = \,\,\,{{\,20\,\,{\rm{feet }}} \over {0.5\,\,{\rm{s}}}}\left( {{{1\,\,{\rm{mile}}} \over {5280\,\,{\rm{feet}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\left( {{{60\,\,{\rm{s}}} \over {1\,\,{\rm{min}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\left( {{{60\,\,{\rm{min}}} \over {1\,\,{\rm{h}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\,\, = \,\,\,{{\,20\,\, \cdot \,\,60\,\, \cdot \,\,60\,} \over {0.5\,\, \cdot \,\,5280}}\,\,\,\,\left[ {{\rm{mph}}} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( A \right)\)
Obs.: arrows indicate
licit converters.
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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