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26 Mar 2019, 10:58
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:37) correct
41%
(01:35)
wrong
based on 323
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GMATH practice exercise (Quant Class 19)
Two trains travel at constant speeds. What is the ratio of the slower speed to the faster speed?
(1) The time it takes for one train to pass the other when they are in the same direction is 3h.
(2) The time it takes for one train to pass the other when they are in opposite directions is 2h.
Two trains travel at constant speeds. What is the ratio of the slower speed to the faster speed?
(1) The time it takes for one train to pass the other when they are in the same direction is 3h.
(2) The time it takes for one train to pass the other when they are in opposite directions is 2h.
26 Mar 2019, 15:10
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fskilnik
\({\rm{faster}}\,\,{\rm{train}}\,\,\left\{ \matrix{\\
\,x\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr \\
\,A\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.\)
\({\rm{slower}}\,\,{\rm{train}}\,\,\left\{ \matrix{\\
\,y\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr \\
\,B\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.\)
\(? = {B \over A}\,\,\,\,\,\,\,\left[ {A > B > 0} \right]\)
\(\left. \matrix{\\
\left( 1 \right)\,\,A - B = {{y + x} \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{trivial}}\,\,{\rm{bifurcation}}\,\, \hfill \cr \\
\left( 2 \right)\,\,A + B = {{y + x} \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{trivial}}\,\,{\rm{bifurcation}} \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {1 + 2} \right)} \,\,\,\,3\left( {A - B} \right) = 2\left( {A + B} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,A = 5B\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)
The correct answer is (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
24 Nov 2020, 00:35
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Hi and thanks for your question.
How is one expected to know the trains are disposed in space as you show in your drawing?
IMO there is no detail about what is the starting point from which the trains start moving, the distance among them could be non-zero as far as we know.
Hence, answer should be E
Please, let me know if unclear/ what I'm getting wrong! Thanks
How is one expected to know the trains are disposed in space as you show in your drawing?
IMO there is no detail about what is the starting point from which the trains start moving, the distance among them could be non-zero as far as we know.
Hence, answer should be E
Please, let me know if unclear/ what I'm getting wrong! Thanks
