BTGmoderatorDC wrote:Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
A. 12
B. 20
C. 24
D. 30
E. 36
Source: Economist GMAT
Perfect opportunity for UNITS CONTROL, one of the most powerful tools of our method!
$$LCM\left( {36,60} \right) = 180\,\,\,\,\left\{ \matrix{
\,A \to C\,\,\,:\,\,\,180\,\,{\rm{miles}}\,\,\,\left( {{{1\,\,{\rm{hour}}} \over {36\,\,{\rm{miles}}}}} \right)\,\,\,\,\, = \,\,\,5\,\,{\rm{hours}}\, \hfill \cr
\,A \to B\,\,\,:\,\,\,{2 \over 3}\left( {180\,\,{\rm{miles}}} \right)\left( {{{1\,\,{\rm{hour}}} \over {60\,\,{\rm{miles}}}}} \right)\,\,\, = \,\,2\,\,{\rm{hours}}\,\,\, \hfill \cr
B \to C\,\,\,:\,\,\,\,\,\,\,\,?\,\, = \,\,{{{1 \over 3}\left( {180\,\,{\rm{miles}}} \right)} \over {5 - 2\,\,{\rm{hours}}}}\,\,\, = \,\,\,\,20\,\,{\rm{mph}} \hfill \cr} \right.\,\,\,$$
This solution follows the notations and rationale taught in the GMATH course.
Regards,
Fabio.
