EgmatQuantExpert wrote:
A bus completed first 50 miles of a 120-mile trip at an average speed of 20 mph. Then it took a halt of 30 minutes and completed the half of the remaining journey at an average speed of 35 mph. At what average speed it should complete the remaining journey so that the overall average speed of the whole journey becomes 20 mph?
A. 40 mph
B. 35 mph
C. 30 mph
D. 22.5 mph
E. 17.5 mph
Excellent opportunity for
UNITS CONTROL, one of the most powerful tools of our method!
\(? = x\,\,{\rm{mph}}\,\,\,\left( {{\rm{final}}\,\,{\rm{miles}}} \right)\)
\(120\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {20\,\,{\rm{miles}}}}} \right)\,\,\,\, = \,\,\,\,6\,{\rm{h}}\,\,\,\, \to \,\,\,\,{\rm{trip}}\,\,{\rm{total}}\,\,{\rm{time}}\,\,\)
\(\left. \matrix{
50\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {20\,\,{\rm{miles}}}}} \right)\,\,\,\, = \,\,\,\,2.5\,{\rm{h}}\,\,\,\, \to \,\,\,\,\,{\rm{first}}\,\,{\rm{distance}}\,\,{\rm{time}}\,\,\,\, \hfill \cr
{1 \over 2}{\rm{h}}\,\,\,\, \to \,\,\,\,\,{\rm{halt}}\,\,{\rm{time}} \hfill \cr} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,6 - \left( {2.5 + 0.5} \right) = 3{\mathop{\rm h}\nolimits} \,\,\,\,{\rm{last}}\,\,{\rm{distance}}\,\,\left( {120 - 50 = 70\,\,{\rm{miles}}} \right)\,\,{\rm{time}}\)
\({{70} \over 2}\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {35\,\,{\rm{miles}}}}} \right)\,\,\,\, = \,\,\,\,1\,{\rm{h}}\,\,\,\, \to \,\,\,\,\,{\rm{last}}\,\,\underline {{\rm{half}}} \,\,{\rm{distance}}\,\,{\rm{time}}\)
\({\rm{Last}}\,\,{\rm{2}}\,\,{\rm{h}}\,\,{\rm{for}}\,\,35\,\,{\rm{miles}}\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = x = {{30 + 5} \over 2}\,\,{\rm{ = }}\,\,{\rm{17}}{\rm{.5}}\,\,{\rm{mph}}\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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