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)

Our high-level "quant" preparation starts here: https://gmath.net