swerve wrote:Greg is training for a marathon by running to and from work each day, a distance of 12 miles each way. He runs from home to work at an average speed of 6 miles per hour and returns at an average speed of 4 miles per hour. What is Greg's average speed, in miles per hour, for the round trip?
A. 5.5
B. 5.0
C. 4.8
D. 2.5
E. 2.4
Source: Princeton Review
Let´s use UNITS CONTROL, one of the most powerful tools of our method!
$$? = {{{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{miles}}} \over {{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}}}$$
$$12\,\,{\rm{miles}}\,\,\,\,\left\{ \matrix{
\,\,{\rm{home - work}}:\,\,\,12\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {\,6\,\,{\rm{miles}}\,}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\,\,\,\, = \,\,2\,{\rm{h}} \hfill \cr
\,\,{\rm{work - home}}:\,\,\,12\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {\,4\,\,{\rm{miles}}\,}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\, = \,\,3\,{\rm{h}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}\,\,\, = \,\,5\,\,{\rm{h}}$$
Obs.: arrows indicate
licit converters.
$$? = {{2 \cdot 12} \over 5} = {{20 + 4} \over 5} = 4{4 \over 5}\,\, = \,\,4.8\,\,\,\,\,\left[ {{\rm{mph}}} \right]$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
